|
%I #10 May 08 2018 02:43:02
%S 1,3210,3498,3882,6453804,7873684,7943640,8028120,8099880,9112230,
%T 9561990,10079430,182626920,192651480,196192920,199939320,200271960,
%U 201632760,203289240,206367480,206645880,207815160,208955160,210368760,210406680,210717720,211645560
%N Numbers whose sum of divisors is the fifth power of one of their divisors.
%C Subset of A019423.
%e Divisors of 3210 are 1, 2, 3, 5, 6, 10, 15, 30, 107, 214, 321, 535, 642, 1070, 1605, 3210 and their sum is 7776 = 6^5.
%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]^5 then print(n); break; fi; od; od; end: P(10^9);
%t Select[Range[10^4], IntegerQ[t = DivisorSigma[1, #]^(1/5)] && Mod[#, t] == 0 &] (* _Giovanni Resta_, May 04 2018 *)
%o (PARI) isok(n) = (n==1) || (ispower(s=sigma(n), 5) && !(n % sqrtnint(s, 5))); \\ _Michel Marcus_, May 05 2018
%Y Cf. A000203, A019423, A303123, A303993, A303994, A303996.
%K nonn
%O 1,2
%A _Paolo P. Lava_, May 04 2018
%E a(13)-a(27) from _Giovanni Resta_, May 04 2018
|
