A086417 Sum of divisors of 3-smooth numbers.

1, 3, 4, 7, 12, 15, 13, 28, 31, 39, 60, 40, 63, 91, 124, 120, 127, 195, 121, 252, 280, 255, 403, 363, 508, 600, 364, 511, 819, 847, 1020, 1240, 1092, 1023, 1651, 1815, 1093, 2044, 2520, 2548, 2047, 3315, 3751, 3279, 4092, 5080, 5460, 4095, 3280

Offset: 1

Author

Reinhard Zumkeller, Jul 18 2003

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A086416.

Cf. A000203, A003586, A022328, A022329.

Programs

Haskell

a086417 n = (2 ^ (a022328 n + 1) - 1) * (3 ^ (a022329 n + 1) - 1) `div` 2
-- Reinhard Zumkeller, Nov 19 2015

Mathematica

DivisorSigma[1,#]&/@Select[Range[4000],Max[FactorInteger[#][[All,1]]]<4&] (* Harvey P. Dale, Feb 14 2017 *)

Formula

a(n) = A000203(A003586(n));

a(n) = (2^(A022328(n)+1)-1)*(3^(A022329(n)+1)-1)/2.

a(n) = A000225(j) * A003462(k) for some j,k > 0. - Flávio V. Fernandes, May 29 2021