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A373459 Expansion of Sum_{p prime} x^p/(1 - (p*x)^p).

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%I A373459 #14 Mar 30 2025 09:56:37
%S A373459 0,1,1,4,1,43,1,64,729,3381,1,20707,1,827639,10297066,16384,1,
%T A373459 14414443,1,30517840269,678610493338,285312719187,1,10464547507,
%U A373459 95367431640625,302875123369469,282429536481,558545864150392871,1,298030849742873568,1,1073741824
%N A373459 Expansion of Sum_{p prime} x^p/(1 - (p*x)^p).
%F A373459 a(n) = Sum_{p|n prime} p^(n - p).
%F A373459 If p is prime, a(p) = 1.
%t A373459 a[n_]:=Sum[Boole[PrimeQ[d]]d^(n-d),{d,Divisors[n]}]; Array[a,32] (* _Stefano Spezia_, Mar 30 2025 *)
%o A373459 (PARI) a(n) = sumdiv(n, d, isprime(d)*d^(n-d));
%Y A373459 Cf. A200768, A373458.
%K A373459 nonn,easy
%O A373459 1,4
%A A373459 _Seiichi Manyama_, Jun 06 2024