cp's OEIS Frontend

A303999 Numbers whose sum of divisors is the seventh power of one of their divisors.

%I A303999 #12 May 09 2018 08:19:36
%S A303999 1,112890,120054,124338,133998,137058,139962,36705396,39118548,
%T A303999 52166212,4661585292,4677211812,4851457716,4968055596,6168611160,
%U A303999 6232929480,6236525932,6261521812,6311227560,6362855640,6430524120,6468862876,6488003880,6500134440,6506266732
%N A303999 Numbers whose sum of divisors is the seventh power of one of their divisors.
%C A303999 Subset of A048257.
%e A303999 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 A303999 with(numtheory): P:=proc(q) local a,k,n;
%p A303999 for n from 1 to q do a:=sort([op(divisors(n))]);
%p A303999 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 A303999 Select[Range[150000], IntegerQ[t = DivisorSigma[1, #]^(1/7)] && Mod[#, t] == 0 &] (* _Giovanni Resta_, May 04 2018 *)
%o A303999 (PARI) isok(n) = (n==1) || (ispower(s=sigma(n), 7) && !(n % sqrtnint(s, 7))); \\ _Michel Marcus_, May 05 2018
%Y A303999 Cf. A000203, A048257, A303123, A303993, A303994, A303995, A303996.
%K A303999 nonn,easy
%O A303999 1,2
%A A303999 _Paolo P. Lava_, May 04 2018
%E A303999 a(11)-a(25) from _Giovanni Resta_, May 04 2018