A359112 a(n) = Sum_{d|n} (n/d) * d^(n-d).

1, 3, 4, 13, 6, 109, 8, 777, 2197, 7541, 12, 374809, 14, 1675773, 31954096, 100794385, 18, 7391871271, 20, 163547770441, 2037381161992, 570634875581, 24, 1275177760626097, 476837158203151, 605750431288341, 450286447756825720, 2258377795760750777, 30

Offset

1,2

Links

Table of n, a(n) for n=1..29.

Formula

G.f.: Sum_{k>=1} x^k/(1 - (k * x)^k)^2.

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

Mathematica

a[n_] := DivisorSum[n, #^(n-#)*n/# &]; Array[a, 29] (* Amiram Eldar, Aug 27 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, n/d*d^(n-d));
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-(k*x)^k)^2))

Crossrefs

Cf. A000203, A167531.

Cf. A082245, A342628.

Sequence in context: A127611 A308688 A324501 * A342675 A330158 A082197

Adjacent sequences: A359109 A359110 A359111 * A359113 A359114 A359115

Keyword

nonn

Author

Seiichi Manyama, Dec 17 2022

Status

approved