A342629 a(n) = Sum_{d|n} (n/d)^(n-d).
1, 3, 10, 69, 626, 7866, 117650, 2101265, 43047451, 1000390658, 25937424602, 743069105634, 23298085122482, 793728614541474, 29192926269590300, 1152925902670135553, 48661191875666868482, 2185913413229070900339, 104127350297911241532842
Offset: 1
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..387
Programs
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Mathematica
a[n_] := DivisorSum[n, (n/#)^(n - #) &]; Array[a, 20] (* Amiram Eldar, Mar 17 2021 *)
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PARI
a(n) = sumdiv(n, d, (n/d)^(n-d));
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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))) -
Python
from sympy import divisors def A342629(n): return sum((n//d)**(n-d) for d in divisors(n,generator=True)) # Chai Wah Wu, Jun 19 2022
Formula
G.f.: Sum_{k>=1} k^(k-1) * x^k/(1 - k^(k-1) * x^k).
If p is prime, a(p) = 1 + p^(p-1).