

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
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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.


MATHEMATICA

nn = 10^6; maxd = 0;
Reap[For[n = 1, n <= nn, n += 2, If[(nd = DivisorSigma[0, n]) > maxd, Print[n]; Sow[n]; maxd = nd]]][[2, 1]] (* JeanFrançois Alcover, Sep 20 2018, from PARI *)


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



