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A342370 a(n) = Sum_{k=1..n} gcd(k,n)^(k-1).

%I A342370 #44 Mar 14 2021 07:36:48
%S A342370 1,3,11,68,629,7797,117655,2097254,43046979,1000000799,25937424611,
%T A342370 743008402000,23298085122493,793714773374529,29192926027528343,
%U A342370 1152921504613147242,48661191875666868497,2185911559739107208115,104127350297911241532859,5242880000000008181608132
%N A342370 a(n) = Sum_{k=1..n} gcd(k,n)^(k-1).
%H A342370 Martin Ehrenstein, <a href="/A342370/b342370.txt">Table of n, a(n) for n = 1..400</a>
%F A342370 If p is prime, a(p) = p-1 + p^(p-1) = A173235(p).
%t A342370 a[n_] := Sum[GCD[k, n]^(k - 1), {k, 1, n}]; Array[a, 20] (* _Amiram Eldar_, Mar 13 2021 *)
%o A342370 (PARI) a(n) = sum(k=1, n, gcd(k, n)^(k-1));
%Y A342370 Cf. A000010, A018804, A056665, A173235, A341036, A342394, A342433, A342436, A342449.
%K A342370 nonn
%O A342370 1,2
%A A342370 _Seiichi Manyama_, Mar 13 2021
%E A342370 a(19) and beyond from _Martin Ehrenstein_, Mar 13 2021