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%I #14 Sep 08 2022 08:45:38
%S 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,
%T 80,81,84,90,96,100,105,108,112,120,125,126,128,135,140,144,150,160,
%U 162,168,175,180,189,192,196,200,210,216,224,225,240,243,245,250,252,256
%N Numbers k such that Product{i=1..k}[sigma_0(i)] / k is an integer.
%C A066843(k)/A000027(k) is an integer.
%H Harvey P. Dale, <a href="/A146982/b146982.txt">Table of n, a(n) for n = 1..1000</a>
%t With[{nn=300},Select[Thread[{FoldList[Times,DivisorSigma[0,Range[ nn]]], Range[ nn]}], IntegerQ[#[[1]]/#[[2]]]&]][[All,2]] (* _Harvey P. Dale_, Mar 05 2019 *)
%o (Magma) [ n: n in [1..260] | &*[ NumberOfDivisors(k): k in [1..n] ] mod n eq 0 ]; // _Klaus Brockhaus_, Nov 05 2008
%o (PARI) isok(k) = frac(prod(i=1, k, numdiv(i))/k) == 0; \\ _Michel Marcus_, Feb 06 2018
%Y Cf. A066843, A000005, A000027.
%K nonn
%O 1,2
%A _Ctibor O. Zizka_, Nov 04 2008
%E Extended beyond a(12) by _Klaus Brockhaus_, Nov 05 2008
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