In mathematics, a deficient number is a positive integer that is smaller than the sum of its proper divisors. Conversely, a magic number is a positive integer that is equal to the sum of its proper divisors. The term "deficient" refers to the fact that such numbers are "deficient" or lacking when compared to a magic number. A N/deficient number is a positive integer N that is both deficient and a magic number. In other words, it has the property that the sum of its proper divisors is equal to N, and N is smaller than the sum of the proper divisors of any other positive integer. For example, the number 12 is a magic number because the sum of its proper divisors (1, 2, 3, 4, 6) is equal to 12.
Oct. 1: Cubs, 3:10 p.m., EST
The material on this site may not be reproduced, distributed, transmitted, cached or otherwise used, except with the prior written permission of Advance Local. -- The Marlins have a half-game lead over the Cubs for the final NL wild-card spot after a long night in New York that ended with their game with the Mets being suspended just before 1 a.
For example, the number 12 is a magic number because the sum of its proper divisors (1, 2, 3, 4, 6) is equal to 12. However, it is also a deficient number because it is smaller than the sum of the proper divisors of other integers, such as 24 (1+2+3+4+6+8+12 = 36 > 24). The concept of N/deficient numbers has interesting properties and applications in number theory and mathematics.
MLB magic numbers: Aroldis Chapman blows up, Mariners walk-off Rangers; Orioles clinch (9/29/23)
Yankees fans were sick of Aroldis Chapman even before he quit on his team last year when finding out he’d be left off the playoff roster.
They remember the Cuban Missile’s playoff blowups, especially Jose Altuve’s walk-off that sent the Astros to the World Series in 2019.
Two teams later, Chapman wasn’t clutch again Thursday night for the Rangers, who blew a chance to clinch a tie for the AL West title when a 2-1 ninth-inning lead turned into a 3-2 loss to the wild-card contending Mariners.
Chapman entered for the ninth looking for a save and then allowed two singles threw a wild pitch and issued a walk to load the bases with nobody out.
That was it for Chapman, who was replaced by Jonathan Hernandez. After a flyout to center and popup to third, JP Crawford laced a two-run double for a walk-off win that jumped the Mariners to one game behind the Astros for the final wild-card spot instead of falling two back with three to play.
The Rangers lead the Astros by a game for first in the division.
The Mariners and Rangers end the regular season this weekend with a series in Seattle. The Astros will be in Arizona to play the Diamondbacks, who are in the second NL wild-card position.
Elsewhere on Thursday …
-- The Orioles won the AL East and locked up the top seed in the American League with a 2-0 win over the Red Sox at Oriole Park. This is a first division title since 2014 for Baltimore, which led from the first inning on courtesy of a solo homer by Anthony Santander.
-- The Marlins have a half-game lead over the Cubs for the final NL wild-card spot after a long night in New York that ended with their game with the Mets being suspended just before 1 a.m., after a 3-hour, 17-minute rain delay. The Marlins trailed 1-0 after eight innings, scored two in the ninth and then the game stopped while they was still batting. If necessary, the Marlins and Mets probably will complete their game on Monday.
-- The Cubs lost ground to the Marlins by losing 5-3 in Atlanta.
Here are MLB magic numbers and remaining schedules for contenders through Thursday, Sept. 28, along with playoff matchups if Wild Card Series began Friday:
BALTIMORE ORIOLES (100-59)
Standings: First in AL East. Lead Rays by 3 games.
Magic number to clinch AL East: Clinched Sept. 28.
Games remaining: 3 (3 home).
Orioles schedule:
Sept. 29: Red Sox, 7:05 p.m., EST
Sept. 30: Red Sox, 7:15 p.m., EST
Oct. 1: Red Sox, 3:05 p.m., EST
TAMPA BAY RAYS (97-62)
Standings: Second in AL East. Trail Orioles by 3 games. Clinched first AL wild card.
Magic number to clinch playoffs: Sept. 17.
Games remaining: 3 (3 road).
Rays schedule:
Sept. 29: at Blue Jays, 7:07 p.m., EST
Sept. 30: at Blue Jays, 3:07 p.m., EST
Oct. 1: at Blue Jays, 3:07 p.m., EST
TORONTO BLUE JAYS (88-71)
Standings: Third in AL East. Lead Astros by 1 game for second AL wild card. Lead Mariners by 2 games for third AL wild card.
Magic number to clinch playoffs: 2
Remaining games: 3 (3 home).
Blue Jays schedule:
Sept. 29: Rays, 7:07 p.m., EST
Sept. 30: Rays, 3:07 p.m., EST
Oct. 1: Rays, 3:07 p.m., EST
MINNESOTA TWINS (85-74)
Standings: First in AL Central. Lead second-place Guardians by 10 games.
Magic number to clinch AL Central: Clinched Sept. 22.
Remaining games: 3 (3 road).
Twins schedule:
Sept. 29: at Rockies, 8:10 p.m.
Sept. 30: at Rockies, 8:10 p.m.
Oct. 1: at Rockies, 3:10 p.m.
TEXAS RANGERS (89-70)
Standings: First in AL West. Lead second-place Astros by 2 games. Astros hold tiebreaker.
Magic number to clinch AL Central: 2
Magic number to clinch playoffs: 1
Remaining games: 3 (3 road).
Rangers schedule:
Sept. 29: at Seattle, 10:10 p.m., EST
Sept. 30: at Seattle, 7:15 p.m., EST
Oct. 1: at Seattle, 3:10 p.m., EST
HOUSTON ASTROS (87-72)
Standings: Second in AL West. Trail first-place Rangers by 2 games. Lead Mariners by 1 game for third AL wild card.
Magic number to clinch playoffs: 3
Remaining games: 3 (3 road).
Astros schedule:
Sept. 29: at Arizona, 9:40 p.m., EST
Sept. 30: at Arizona, 8:10 p.m., EST
Oct. 1: at Arizona, 3:10 p.m., EST
SEATTLE MARINERS (85-73)
Standings: Third in AL West. Trail first-place Rangers by 3 games. Trail Astros by 1 game for third AL wild card.
Magic number for playoffs elimination: 3
Remaining games: 3 (3 home)
Mariners schedule:
Sept. 29: Rangers, 10:10 p.m., EST
Sept. 30: Rangers, 7:15 p.m., EST
Oct. 1: Rangers, 3:10 p.m., EST
ATLANTA BRAVES (103-56)
Standings: First in NL East. Lead second-place Phillies by 14 games. Clinched first seed in NL.
Magic number to clinch NL East: Clinched Sept. 13.
Remaining games: 3 (3 home).
Braves schedule:
Sept. 29: Nationals, 7:20 p.m., EST
Sept. 30: Nationals, 7:20 p.m., EST
Oct. 1: Nationals, 7:20 p.m., EST
Standings: Second in NL East. Clinched first NL wild card.
Magic number to clinch playoffs: Clinched Sept. 26.
Remaining games: 3 (3 road).
Phillies schedule:
Sept. 29: at Mets, 7:10 p.m., EST
Sept. 30: at Mets, 7:10 p.m., EST
Oct. 1: at Mets, 3:10 p.m., EST
MIAMI MARLINS (82-76)
Standings: Third in NL East. Lead Cubs by 0.5 games for third NL wild card. Marlins hold tiebreaker.
Magic number to clinch playoffs: 4
Remaining games: 4 (4 road).
Marlins schedule:
Sept. 29: at Pirates, 6:35 p.m., EST
Sept. 30: at Pirates, 6:35 p.m., EST
Oct. 1: at Pirates, 4:05 p.m., EST
Oct. 2: at Mets, if necessary, completion of suspended game from Sept. 28.
MILWAUKEE BREWERS (90-69)
Standings: First in NL Central. Lead second-place Cubs by 8 games.
Magic number to clinch NL Central: Clinched Sept. 26.
Remaining games: 3 (3 home).
Brewers schedule:
Sept. 29: Cubs, 8:10 p.m., EST
Sept. 30: Cubs, 7:10 p.m., EST
Oct. 1: Cubs, 3:10 p.m., EST
CHICAGO CUBS (82-77)
Standings: Second in NL Central. Trail Marlins by 0.5 games for third NL wild card. Marlins hold tiebreaker.
Magic number for playoffs elimination: 4
Remaining games: 3 (3 road).
Cubs schedule:
Sept. 29: at Brewers, 8:10 p.m., EST
Sept. 30: at Brewers, 8:10 p.m., EST
Oct. 1: at Brewers, 8:10 p.m., EST
CINCINNATI REDS (81-78)
Standings: Third in NL Central. Trail Marlins by 1.5 games for third NL wild card.
Magic number for playoffs elimination: 3
Remaining games: 3 (3 road).
Reds schedule:
Sept. 29: at Cardinals, 8:15 p.m., EST
Sept. 30: at Cardinals, 8:15 p.m., EST
Oct. 1: at Cardinals, 3:15 p.m., EST
LOS ANGELES DODGERS (98-61)
Standings: First in NL West. Lead second-place Diamondbacks by 14 games.
Magic number to clinch NL West: Clinched Sept. 17.
Remaining games: 3 (3 road).
Dodgers schedule:
Sept. 29: at Giants, 10:15 p.m., EST
Sept. 30: at Giants, 9:05 p.m., EST
Oct. 1: at Giants, 3:05 p.m., EST
ARIZONA DIAMONDBACKS (84-75)
Standings: Second in NL West. Lead Marlins 1.5 games for second NL wild card. Lead Cubs by 2 games for third NL wild card.
Magic number to clinch playoffs: 3
Remaining games: 3 (3 home).
Diamondbacks schedule:
Sept. 29: Astros, 9:40 p.m., EST
Sept. 30: Astros, 8:10 p.m., EST
Oct. 1: Astros, 3:10 p.m., EST
CURRENT POSTSEASON MATCHUPS
AL WILD CARD SERIES (best-of-3)
Baltimore Orioles (1), Texas Rangers (2) byes
Houston Astros (6) at Minnesota Twins (3)
Toronto Blue Jays (5) at Tampa Bay Rays (4)
NL WILD CARD SERIES (best-of-3)
Atlanta Braves (1), Los Angeles Dodgers (2) byes
Miami Marlins (6) at Milwaukee Brewers (3)
Arizona Diamondbacks (5) at Philadelphia Phillies (4)
Note: Higher seed will host all games (from Tuesday Oct. 3 to Thursday, Oct. 5).
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For example, these numbers can be used in cryptography to generate secure encryption keys or to create random numbers in computer simulations. In conclusion, N/deficient numbers are positive integers that are both deficient and magic numbers. They have unique properties and find applications in various fields of mathematics and computer science..
Reviews for "Nj Defils Magic Number and Its Role in Modern Mathematics"
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