A376014 a(n) = Sum_{d|n} d^d * binomial(n/d,d).

1, 2, 3, 8, 5, 18, 7, 32, 36, 50, 11, 180, 13, 98, 285, 384, 17, 702, 19, 1480, 966, 242, 23, 5640, 3150, 338, 2295, 9352, 29, 22440, 31, 18432, 4488, 578, 65660, 85500, 37, 722, 7761, 229560, 41, 337302, 43, 85448, 406080, 1058, 47, 1449360, 823592, 788750, 18411

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

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

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

Prog

(PARI) a(n) = sumdiv(n, d, d^d*binomial(n/d, d));
(PARI) my(N=60, x='x+O('x^N)); Vec(sum(k=1, N, (k*x^k)^k/(1-x^k)^(k+1)))
(Python)
from math import comb
from itertools import takewhile
from sympy import divisors
def A376014(n): return sum(d**d*comb(n//d, d) for d in takewhile(lambda d:d**2<=n, divisors(n))) # Chai Wah Wu, Sep 06 2024

Crossrefs

Cf. A062796, A338694, A376018.

Sequence in context: A095164 A075384 A072500 * A208449 A346957 A062956

Adjacent sequences: A376011 A376012 A376013 * A376015 A376016 A376017

Keyword

nonn

Author

Seiichi Manyama, Sep 06 2024

Status

approved