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A308668 a(n) = Sum_{d|n} d^(n/d+n). 3
1, 9, 82, 1089, 15626, 287010, 5764802, 135270401, 3487315843, 100244173394, 3138428376722, 107072686593858, 3937376385699290, 155601328490478978, 6568412173896940652, 295165920677390712833, 14063084452067724991010 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

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

G.f.: Sum_{k>=1} k^(k+1) * x^k/(1 - k^(k+1) * x^k). - Seiichi Manyama, Mar 17 2021

MATHEMATICA

a[n_] := DivisorSum[n, #^(n/# + n) &]; Array[a, 20] (* Amiram Eldar, Mar 17 2021 *)

PROG

(PARI) a(n) = sumdiv(n, d, d^(n/d+n));

(PARI) my(N=20, x='x+O('x^N)); Vec(x*deriv(-log(prod(k=1, N, (1-k*(k*x)^k)^(1/k)))))

(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^(k+1)*x^k/(1-k^(k+1)*x^k))) \\ Seiichi Manyama, Mar 17 2021

(Python)

from sympy import divisors

def A308668(n): return sum(d**(n//d+n) for d in divisors(n, generator=True)) # Chai Wah Wu, Jun 19 2022

CROSSREFS

Diagonal of A308502.

Cf. A152211, A294956, A308594.

Sequence in context: A294956 A294645 A338663 * A308481 A041146 A320991

Adjacent sequences: A308665 A308666 A308667 * A308669 A308670 A308671

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jun 16 2019

STATUS

approved

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Last modified December 4 07:45 EST 2022. Contains 358544 sequences. (Running on oeis4.)