A338694 a(n) = Sum_{d|n} d^d * binomial(d, n/d).

1, 8, 81, 1028, 15625, 280017, 5764801, 134219264, 3486784428, 100000031250, 3138428376721, 106993206079936, 3937376385699289, 155568095575106627, 6568408355712921875, 295147905179822588160, 14063084452067724991009, 708235345355351624428356, 37589973457545958193355601

Offset

1,2

Links

Winston de Greef, Table of n, a(n) for n = 1..384

Formula

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

If p is prime, a(p) = p^(p+1).

Mathematica

a[n_] := DivisorSum[n, #^# * Binomial[#, n/#] &]; Array[a, 20] (* Amiram Eldar, Apr 24 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, d^d*binomial(d, n/d));
(PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, (k+k*x^k)^k-k^k))

Crossrefs

Cf. A062796, A318636, A318637, A318638, A338693.

Sequence in context: A210127 A007778 A065440 * A318047 A338685 A092366

Adjacent sequences: A338691 A338692 A338693 * A338695 A338696 A338697

Keyword

nonn

Author

Seiichi Manyama, Apr 24 2021

Status

approved