cp's OEIS Frontend

A342628 a(n) = Sum_{d|n} d^(n-d).

%I A342628 #22 Jun 19 2022 15:23:09
%S A342628 1,2,2,6,2,45,2,322,731,3383,2,132901,2,827641,10297068,33570818,2,
%T A342628 2578617270,2,44812807567,678610493340,285312719189,2,393061010002613,
%U A342628 95367431640627,302875123369471,150094917726535604,569939345952661545,2,105474306078445349841,2
%N A342628 a(n) = Sum_{d|n} d^(n-d).
%H A342628 Seiichi Manyama, <a href="/A342628/b342628.txt">Table of n, a(n) for n = 1..599</a>
%F A342628 G.f.: Sum_{k>=1} x^k/(1 - (k * x)^k).
%F A342628 If p is prime, a(p) = 2.
%t A342628 a[n_] := DivisorSum[n, #^(n - #) &]; Array[a, 30] (* _Amiram Eldar_, Mar 17 2021 *)
%o A342628 (PARI) a(n) = sumdiv(n, d, d^(n-d));
%o A342628 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-(k*x)^k)))
%o A342628 (Python)
%o A342628 from sympy import divisors
%o A342628 def A342628(n): return sum(d**(n-d) for d in divisors(n,generator=True)) # _Chai Wah Wu_, Jun 19 2022
%Y A342628 Cf. A023887, A062796, A308594, A342629.
%K A342628 nonn
%O A342628 1,2
%A A342628 _Seiichi Manyama_, Mar 16 2021