A146982 Numbers k such that Product{i=1..k}[sigma_0(i)] / k is an integer.

1, 2, 4, 6, 8, 9, 12, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 70, 72, 75, 80, 81, 84, 90, 96, 100, 105, 108, 112, 120, 125, 126, 128, 135, 140, 144, 150, 160, 162, 168, 175, 180, 189, 192, 196, 200, 210, 216, 224, 225, 240, 243, 245, 250, 252, 256

Offset: 1

Author

Ctibor O. Zizka, Nov 04 2008

Keywords

• nonn

Comments

A066843(k)/A000027(k) is an integer.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A066843, A000005, A000027.

Programs

Magma

[ n: n in [1..260] | &*[ NumberOfDivisors(k): k in [1..n] ] mod n eq 0 ]; // Klaus Brockhaus, Nov 05 2008

Mathematica

With[{nn=300},Select[Thread[{FoldList[Times,DivisorSigma[0,Range[ nn]]], Range[ nn]}], IntegerQ[#[[1]]/#[[2]]]&]][[All,2]] (* Harvey P. Dale, Mar 05 2019 *)

PARI

isok(k) = frac(prod(i=1, k, numdiv(i))/k) == 0; \\ Michel Marcus, Feb 06 2018

Extensions

Extended beyond a(12) by Klaus Brockhaus, Nov 05 2008