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

5, 22, 23, 102, 110, 382, 497, 510, 517, 527, 719, 1436, 4509, 5039, 6906, 8426, 8786, 9051, 9598, 9741, 9951, 10011, 10505, 10795, 11005, 11431, 11501, 11891, 11995, 12121, 13661, 13777, 13891, 13919, 14101, 14129, 14141, 28780, 31636, 32572, 32756, 33028, 33356

Offset

1,1

Comments

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

Links

Paolo P. Lava, Table of n, a(n) for n = 1..150

Example

sigma(382) = 576 and d(382) * d(382^2) * d(382^3) = 4 * 9 * 16 = 576;
sigma(9598) = 14400 and d(9598) * d(9598^2) * d(9598^3) * d(9598^4) = 4 * 9 * 16 * 25 = 14400.

Maple

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);

Mathematica

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 *)

Crossrefs

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

Sequence in context: A063619 A229801 A045015 * A288676 A085101 A350120

Adjacent sequences: A283755 A283756 A283757 * A283759 A283760 A283761

Keyword

nonn

Author

Paolo P. Lava, Mar 16 2017

Status

approved