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A053624 Highly composite odd numbers (1): where d(n) increases to a record. 11
1, 3, 9, 15, 45, 105, 225, 315, 945, 1575, 2835, 3465, 10395, 17325, 31185, 45045, 121275, 135135, 225225, 405405, 675675, 1576575, 2027025, 2297295, 3828825, 6891885, 11486475, 26801775, 34459425, 43648605, 72747675, 130945815 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also least number k such that the number of partitions of k into consecutive integers is a record. For example, 45 = 22+23 = 14+15+16 = 7+8+9+10+11 = 5+6+7+8+9+10 = 1+2+3+4+5+6+7+8+9, six such partitions, but all smaller terms have fewer such partitions (15 has four). See A000005 comments and A038547 formula. - Rick L. Shepherd, Apr 20 2008

LINKS

Ray Chandler, Table of n, a(n) for n = 1..170

David Ryan, Mathematical Harmony Analysis, arXiv preprint arXiv:1603.08904 [cs.SD], 2016.

EXAMPLE

9 is in list because 9 has 3 divisors {1, 3, 9}, which is more than any previous odd number.

PROG

(PARI) lista(nn) = {maxd = 0; forstep (n=1, nn, 2, if ((nd = numdiv(n)) > maxd, print1(n, ", "); maxd = nd; ); ); } \\ Michel Marcus, Apr 21 2014

CROSSREFS

Cf. A002182, A053640, A000005, A038547. Subsequence of A147516.

Sequence in context: A082702 A214771 A065917 * A119239 A140864 A171929

Adjacent sequences:  A053621 A053622 A053623 * A053625 A053626 A053627

KEYWORD

nonn,nice

AUTHOR

Stefano Lanfranco (lastefano(AT)yahoo.it), Mar 21 2000

STATUS

approved

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Last modified November 23 21:46 EST 2017. Contains 295141 sequences.