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
Keywords
Examples
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.
Links
- Paolo P. Lava, Table of n, a(n) for n = 1..150
Programs
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Maple
with(numtheory): P:=proc(q) local a,k,n; for n from 1 to q do a:=1; k:=0; while a
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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 *)
Comments