A283498 a(n) = Sum_{d|n} d^(d+1).

1, 9, 82, 1033, 15626, 280026, 5764802, 134218761, 3486784483, 100000015634, 3138428376722, 106993205660122, 3937376385699290, 155568095563577034, 6568408355712906332, 295147905179487044617, 14063084452067724991010, 708235345355341163422059, 37589973457545958193355602

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..385

Formula

From Ilya Gutkovskiy, May 06 2017: (Start)

G.f.: Sum_{k>=1} k^(k+1)*x^k/(1 - x^k).

L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^k)) = Sum_{n>=1} a(n)*x^n/n. (End)

Example

a(6) = 1^2 + 2^3 + 3^4 + 6^7 = 280026.

Mathematica

f[n_] := Block[{d = Divisors[n]}, Total[d^(d + 1)]]; Array[f, 19] (* Robert G. Wilson v, Mar 10 2017 *)

Prog

(PARI) a(n) = sumdiv(n, d, d^(d+1)); \\ Michel Marcus, Mar 09 2017
(Python)
from sympy import divisors
def A283498(n): return sum(d**(d+1) for d in divisors(n, generator=True)) # Chai Wah Wu, Jun 19 2022

Crossrefs

Cf. A007778, A062796 (Sum_{d|n} d^d).

Sequence in context: A060531 A248848 A045741 * A294956 A294645 A338663

Adjacent sequences: A283495 A283496 A283497 * A283499 A283500 A283501

Keyword

nonn

Author

Seiichi Manyama, Mar 09 2017

Extensions

More terms from Michel Marcus, Mar 09 2017

Status

approved