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A283758 Numbers whose sum of divisors is equal to the product of the number of divisors of their k first powers, for some k.

%I A283758 #11 Mar 21 2017 04:44:07
%S A283758 5,22,23,102,110,382,497,510,517,527,719,1436,4509,5039,6906,8426,
%T A283758 8786,9051,9598,9741,9951,10011,10505,10795,11005,11431,11501,11891,
%U A283758 11995,12121,13661,13777,13891,13919,14101,14129,14141,28780,31636,32572,32756,33028,33356
%N A283758 Numbers whose sum of divisors is equal to the product of the number of divisors of their k first powers, for some k.
%C A283758 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 A283758 Paolo P. Lava, <a href="/A283758/b283758.txt">Table of n, a(n) for n = 1..150</a>
%e A283758 sigma(382) = 576 and d(382) * d(382^2) * d(382^3) = 4 * 9 * 16 = 576;
%e A283758 sigma(9598) = 14400 and d(9598) * d(9598^2) * d(9598^3) * d(9598^4) = 4 * 9 * 16 * 25 = 14400.
%p A283758 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 A283758 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 A283758 Cf. A000005, A000203, A270389, A270713, A275660, A283757, A283759.
%K A283758 nonn
%O A283758 1,1
%A A283758 _Paolo P. Lava_, Mar 16 2017