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A231563 a(n) = f(1)^n + ... + f(n)^n (mod n) where f(i)=i if gcd(i,n)=1 and f(i)=0 otherwise.

%I A231563 #22 Feb 11 2021 11:16:41
%S A231563 0,1,0,2,0,2,0,4,0,0,0,4,0,0,0,8,0,6,0,8,0,0,0,8,0,0,0,0,0,20,0,16,0,
%T A231563 0,0,12,0,0,0,16,0,12,0,0,0,0,0,16,0,0,0,0,0,18,0,0,0,0,0,16,0,0,0,32,
%U A231563 0,44,0,0,0,0,0,24,0,0,0,0,0,0,0,32,0,0
%N A231563 a(n) = f(1)^n + ... + f(n)^n (mod n) where f(i)=i if gcd(i,n)=1 and f(i)=0 otherwise.
%H A231563 Vincenzo Librandi, <a href="/A231563/b231563.txt">Table of n, a(n) for n = 1..5000</a>
%F A231563 a(n) = A308481(n) mod n. - _Seiichi Manyama_, Feb 11 2021
%t A231563 S[n_] :=  Mod[Sum[If[GCD[i, n] == 1, PowerMod[i, n, n], 0], {i, 1, n}], n]; Array[S,100]
%o A231563 (PARI) f(i, n) = if (gcd(i, n) == 1, i, 0);
%o A231563 a(n) = lift(sum(k=1, n, Mod(f(k, n), n)^n)); \\ _Michel Marcus_, Jul 16 2017
%Y A231563 Cf. A231564, A231565, A308481.
%K A231563 nonn
%O A231563 1,4
%A A231563 _José María Grau Ribas_, Dec 09 2013