A373459 Expansion of Sum_{p prime} x^p/(1 - (p*x)^p).
0, 1, 1, 4, 1, 43, 1, 64, 729, 3381, 1, 20707, 1, 827639, 10297066, 16384, 1, 14414443, 1, 30517840269, 678610493338, 285312719187, 1, 10464547507, 95367431640625, 302875123369469, 282429536481, 558545864150392871, 1, 298030849742873568, 1, 1073741824
Offset: 1
Programs
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Mathematica
a[n_]:=Sum[Boole[PrimeQ[d]]d^(n-d),{d,Divisors[n]}]; Array[a,32] (* Stefano Spezia, Mar 30 2025 *) -
PARI
a(n) = sumdiv(n, d, isprime(d)*d^(n-d));
Formula
a(n) = Sum_{p|n prime} p^(n - p).
If p is prime, a(p) = 1.