A182694 a(n) = the largest 3-digit number with exactly n divisors, a(n) = 0 if no such number exists.

0, 997, 961, 998, 625, 981, 729, 999, 676, 976, 0, 996, 0, 832, 784, 984, 0, 980, 0, 912, 576, 0, 0, 990, 0, 0, 900, 960, 0, 720, 0, 840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,2

Comments

max {n : a(n) > 0} = 32, a(n) = 0 for n > 32.

Links

Table of n, a(n) for n=1..53.

Formula

a(n) = max {99 < k < 1000 : A000005(k)=n} if set is nonempty, else a(n) = 0.

Maple

with (numtheory):
b:= n-> `if` (type (n, integer), n, 0):
a:= n-> b (max (select (x-> tau(x)=n, [$100..999])[])):
seq (a(n), n=1..60);

Mathematica

digits=3; tbl=DivisorSigma[0, Range[10^(digits-1), 10^digits-1]]; t=Table[0, {Max[tbl]}]; offset=10^(digits-1)-1; Do[t[[tbl[[i]]]]=i+offset, {i, Length[tbl]}]; t
(With[{tb=Table[{n, DivisorSigma[0, n]}, {n, 999, 100, -1}]}, Table[ SelectFirst[ tb, #[[2]]==k&], {k, 60}]]/.Missing["NotFound"]->{0, 0}) [[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 02 2019 *)

Crossrefs

Cf. A000005, A182693.

Sequence in context: A028513 A267119 A210315 * A234847 A057698 A106763

Adjacent sequences: A182691 A182692 A182693 * A182695 A182696 A182697

Keyword

nonn,base

Author

Jaroslav Krizek, Nov 27 2010

Extensions

Edited by Alois P. Heinz, Nov 27 2010

Status

approved