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%I #14 Dec 25 2016 02:15:22
%S 1,16,36,48,49,64,81,100,121,144,162,180,196,225,245,256,324,361,400,
%T 432,441,484,500,529,576,605,625,648,676,729,784,841,900,931,980,1024,
%U 1089,1156,1200,1225,1280,1296,1369,1444,1521,1600,1620,1681,1764,1805
%N Numbers n such that sigma_4(n)/sigma_2(n) is an integer but not a prime.
%H Harry J. Smith, <a href="/A066112/b066112.txt">Table of n, a(n) for n=1..1000</a>
%e The sequence includes squares, twice squares (such as 162 and 648), and other numbers (such as 48 and 180). The sigma_4/sigma_2 quotients usually have more than one distinct prime factor. Exception: sigma_4(48)/sigma_2(48) = 5732210/3410 = 1681 = 41^2.
%t Do[s=DivisorSigma[4, n]; z=DivisorSigma[2, n]; If[IntegerQ[s/z]&&!PrimeQ[s/z], Print[n]], {n, 1, 10000}]
%o (PARI) { n=0; for (m=1, 10^9, if (frac(f=sigma(m, 4)/sigma(m, 2)), next); if (!isprime(f), write("b066112.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Feb 01 2010
%Y Cf. A001157, A001159, A046871, A066109-A066111.
%K nonn
%O 1,2
%A _Labos Elemer_, Dec 06 2001
%E Edited by _Jon E. Schoenfield_, Dec 24 2016
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