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Search: id:A027423
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| A027423 |
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Number of positive divisors of n!. |
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+0
43
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| 1, 1, 2, 4, 8, 16, 30, 60, 96, 160, 270, 540, 792, 1584, 2592, 4032, 5376, 10752, 14688, 29376, 41040, 60800, 96000, 192000, 242880, 340032, 532224, 677376, 917280, 1834560, 2332800, 4665600, 5529600, 7864320, 12165120, 16422912
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OFFSET
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0,3
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COMMENT
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It appears that a(n+1)=2*a(n) if n is in A068499. - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 07 2002
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
D. Berend et al., Gaps between consecutive divisors of factorials, Ann. Inst. Fourier, 43 (3) (1993), 569-583.
Paul Erdos, S. W. Graham, Aleksandar Ivic and Carl Pomerance, On the Number of Divisors of n!, in Analytic Number Theory, Proceedings of a Conference in Honor of Heini Halberstam, ed. by B. C. Berndt, H. G. Diamond, A. J. Hildebrand, Birkhauser 1996, pp. 337-355.
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FORMULA
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a(n) <= a(n+1) <= 2*a(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 07 2002
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EXAMPLE
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a(4) = 8 because 4!=24 has precisely eight distinct divisors: 1,2,3,4,6,8,12,24.
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MAPLE
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A027423 := n -> sigma[ 0 ](n!);
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MATHEMATICA
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Table[ DivisorSigma[0, n! ], {n, 0, 35}]
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CROSSREFS
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Sequence in context: A006533 A027559 A135492 this_sequence A140410 A018763 A054517
Adjacent sequences: A027420 A027421 A027422 this_sequence A027424 A027425 A027426
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Glen Burch (gburch(AT)erols.com), Leroy Quet.
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