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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.
2
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
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 *)
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Mar 16 2017
STATUS
approved