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%I #12 May 09 2018 08:19:36
%S 1,112890,120054,124338,133998,137058,139962,36705396,39118548,
%T 52166212,4661585292,4677211812,4851457716,4968055596,6168611160,
%U 6232929480,6236525932,6261521812,6311227560,6362855640,6430524120,6468862876,6488003880,6500134440,6506266732
%N Numbers whose sum of divisors is the seventh power of one of their divisors.
%C Subset of A048257.
%e Divisors of 112890 are 1, 2, 3, 5, 6, 10, 15, 30, 53, 71, 106, 142, 159, 213, 265, 318, 355, 426, 530, 710, 795, 1065, 1590, 2130, 3763, 7526, 11289, 18815, 22578, 37630, 56445, 112890 and their sum is 279936 = 6^7.
%p with(numtheory): P:=proc(q) local a,k,n;
%p for n from 1 to q do a:=sort([op(divisors(n))]);
%p for k from 1 to nops(a) do if sigma(n)=a[k]^7 then print(n); break; fi; od; od; end: P(10^9);
%t Select[Range[150000], IntegerQ[t = DivisorSigma[1, #]^(1/7)] && Mod[#, t] == 0 &] (* _Giovanni Resta_, May 04 2018 *)
%o (PARI) isok(n) = (n==1) || (ispower(s=sigma(n), 7) && !(n % sqrtnint(s, 7))); \\ _Michel Marcus_, May 05 2018
%Y Cf. A000203, A048257, A303123, A303993, A303994, A303995, A303996.
%K nonn,easy
%O 1,2
%A _Paolo P. Lava_, May 04 2018
%E a(11)-a(25) from _Giovanni Resta_, May 04 2018