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A219362 Numbers n such that the product of divisors of sigma(n) is divisible by the product of divisors of n.

%I A219362 #14 Feb 04 2013 14:51:18
%S A219362 1,6,24,28,120,224,270,496,672,864,3375,3724,4320,4680,6048,6200,6860,
%T A219362 8128,10976,11172,13000,14336,15872,18620,26208,27000,29792,30240,
%U A219362 32760,39546,43008,43875,47616,54880,55860,58752,71680,80262,84375,89376,98865,99200
%N A219362 Numbers n such that the product of divisors of sigma(n) is divisible by the product of divisors of n.
%C A219362 That is, numbers such that A007955(n) | A007955(A000203(n)).
%C A219362 F. Luca proved that this sequence is infinite.
%H A219362 Donovan Johnson, <a href="/A219362/b219362.txt">Table of n, a(n) for n = 1..1000</a>
%H A219362 F. Luca, <a href="http://www.emis.de/journals/JIPAM/article284.html?sid=284">On the product of divisors of n and sigma(n)</a>, J. Inequal. Pure Appl. Math., Volume 4, Issue 2, Article 46, 2003.
%t A219362 Select[Range[100000], Mod[Times @@ Divisors[DivisorSigma[1, #]], Times @@ Divisors[#]] == 0 &] (* _T. D. Noe_, Nov 19 2012 *)
%o A219362 (PARI) A007955(n)=if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2))
%o A219362 is(n)=A007955(sigma(n))%A007955(n)==0 \\ _Charles R Greathouse IV_, Feb 04 2013
%Y A219362 Cf. A000203, A007955.
%K A219362 nonn
%O A219362 1,2
%A A219362 _Michel Marcus_, Nov 19 2012