A182696 a(n) = the largest 4-digit number with exactly n divisors, a(n) = 0 if no such number exists.

0, 9973, 9409, 9998, 2401, 9981, 0, 9994, 9025, 9904, 1024, 9999, 4096, 9664, 9801, 9982, 0, 9972, 0, 9968, 7744, 7168, 0, 9975, 1296, 0, 6400, 9920, 0, 9680, 0, 9990, 9216, 0, 5184, 9996, 0, 0, 0, 9936, 0, 9792, 0, 0, 8100, 0, 0, 9828, 0, 9072, 0, 0, 0, 9900, 0, 8640, 0, 0, 0, 9360, 0, 0, 0, 9240

Offset

1,2

Comments

Among all 4-digit numbers, 64 is the maximum number of divisors, so a(64) is the last nonzero term.

Links

Table of n, a(n) for n=1..64.

Formula

A000005(a(n)) = n for a(n) > 0.

Mathematica

tbl=Table[{n, DivisorSigma[0, n]}, {n, 1000, 9999}];
Table[Max[Transpose[Select[tbl, #[[2]]==x&]][[1]]], {x, 70}]/.-\[Infinity]->0//Quiet (* Harvey P. Dale, Dec 02 2010 *)

Crossrefs

Cf. A182695.

Sequence in context: A266917 A031858 A254975 * A126978 A188790 A190832

Adjacent sequences: A182693 A182694 A182695 * A182697 A182698 A182699

Keyword

nonn,base,fini,full

Author

Jaroslav Krizek, Nov 27 2010

Extensions

Edited by Jon E. Schoenfield, Mar 11 2014

Status

approved