A283758 - OEIS

%I #11 Mar 21 2017 04:44:07

%S 5,22,23,102,110,382,497,510,517,527,719,1436,4509,5039,6906,8426,

%T 8786,9051,9598,9741,9951,10011,10505,10795,11005,11431,11501,11891,

%U 11995,12121,13661,13777,13891,13919,14101,14129,14141,28780,31636,32572,32756,33028,33356

%N Numbers whose sum of divisors is equal to the product of the number of divisors of their k first powers, for some k.

%C Values of k: {2, 2, 3, 2, 2, 3, 3, 2, 3, 3, 5, 3, 3, 6, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, ...}. - _Michael De Vlieger_, Mar 17 2017

%H Paolo P. Lava, <a href="/A283758/b283758.txt">Table of n, a(n) for n = 1..150</a>

%e sigma(382) = 576 and d(382) * d(382^2) * d(382^3) = 4 * 9 * 16 = 576;

%e sigma(9598) = 14400 and d(9598) * d(9598^2) * d(9598^3) * d(9598^4) = 4 * 9 * 16 * 25 = 14400.

%p with(numtheory): P:=proc(q) local a,k,n; for n from 1 to q do a:=1; k:=0; while a<sigma(n) do k:=k+1; a:=a*tau(n^k); if sigma(n)=a then print(n); break; fi; od; od; end: P(10^5);

%t Select[Range[2, 40000], Module[{k = 1, d = DivisorSigma[1, #], b}, While[Set[b, Product[DivisorSigma[0, #^j], {j, k}]] < d, k++]; If[b == d, True, False]] &] (* _Michael De Vlieger_, Mar 17 2017 *)

%Y Cf. A000005, A000203, A270389, A270713, A275660, A283757, A283759.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Mar 16 2017