cp's OEIS Frontend

A289384 Numbers k such that the sum of the divisors of k is of the form m^3 + 1.

%I A289384 #21 Sep 12 2017 02:39:42
%S A289384 1,12,68,82,100,730,886,1089,1241,1252,1352,1440,1908,2804,2947,3274,
%T A289384 5598,6078,7414,9123,10135,10164,10804,10809,11143,12756,13456,13468,
%U A289384 15004,21025,23810,24642,25123,26912,26983,34976,37020,40477,45946,48126,55964,56764
%N A289384 Numbers k such that the sum of the divisors of k is of the form m^3 + 1.
%C A289384 Perfect squares in the sequence are 1, 100, 1089, 13456, 21025, ...
%H A289384 Robert G. Wilson v, <a href="/A289384/b289384.txt">Table of n, a(n) for n = 1..1510</a>
%e A289384 730 is in the sequence because sigma(730) = 1332 = 11^3 + 1.
%p A289384 a:= proc(n) option remember; local k;
%p A289384       for k from 1+`if`(n=1, 0, a(n-1)) while (t->t<>
%p A289384       iroot(t, 3)^3)(numtheory[sigma](k)-1) do od; k
%p A289384     end:
%p A289384 seq(a(n), n=1..40);  # _Alois P. Heinz_, Jul 04 2017
%t A289384 fQ[n_] := ! PrimeQ@n && Block[{sd = DivisorSigma[1, n]}, IntegerQ[(sd - 1)^(1/3)]]; Select[Range@59323, fQ] (* _Robert G. Wilson v_, Jul 05 2017 *)
%o A289384 (PARI) isok(n) = ispower(sigma(n)-1, 3); \\ _Michel Marcus_, Jul 05 2017
%Y A289384 Cf. A000203, A001093, A289290.
%K A289384 nonn
%O A289384 1,2
%A A289384 _Michel Lagneau_, Jul 04 2017
%E A289384 More terms from _Alois P. Heinz_, Jul 04 2017