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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
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.
Sequence in context: A294956 A294645 A338663 * A308481 A041146 A320991
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 16 2019
STATUS
approved

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Last modified April 14 07:58 EDT 2024. Contains 371655 sequences. (Running on oeis4.)