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%I #7 Aug 27 2013 10:47:43
%S 3,7,6,22,19,14,12,21,22,27,43,33,198,28,24,66,67,30,98,57,44,197,367,
%T 42,343,63,85,91,463,54,48,93,86,202,76,66,511,111,99,120,163,60,1285,
%U 129,88,274,751,105,364,199,134,198,211,102,763,84,147,346,1765
%N Smallest number k such that the sum of divisors of k equals n times a square > 1.
%C Smallest k such that sigma(k) = n*q^2.
%H Michel Lagneau, <a href="/A213401/b213401.txt">Table of n, a(n) for n = 1..1500</a>
%e a(8) = 21 because the sum of the divisors of 21 is 1 + 3 + 7 +21 = 32 = 8*4 where 4 is a square.
%p a:= proc(n) local k, p;
%p for k from 1 while irem(sigma(k), n, 'p')>0 or
%p sqrt(p)<>floor(sqrt(p)) or p=1 do od; k
%p end:
%p seq (a(n), n=1..100);
%t snk[n_]:=Module[{k=2,c},c=Sqrt[DivisorSigma[1,k]/n];While[!IntegerQ[c] || c==1,k++;c=Sqrt[DivisorSigma[1,k]/n]];k]; Array[snk,60] (* _Harvey P. Dale_, Aug 27 2013 *)
%Y Cf. A000203, A090688, A213386.
%K nonn
%O 1,1
%A _Michel Lagneau_, Jun 10 2012