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a(n) = Sum_{k=1..n} gcd(k,n)^(gcd(k,n) - 2).
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%I #11 Mar 12 2021 09:11:58

%S 1,2,5,19,129,1303,16813,262166,4782981,100000133,2357947701,

%T 61917365564,1792160394049,56693912392115,1946195068359645,

%U 72057594038190124,2862423051509815809,121439531096599037355

%N a(n) = Sum_{k=1..n} gcd(k,n)^(gcd(k,n) - 2).

%F a(n) = Sum_{d|n} phi(n/d) * d^(d-2).

%t a[n_] := Sum[GCD[k, n]^(GCD[k, n] - 2), {k, 1, n}]; Array[a, 20] (* _Amiram Eldar_, Mar 12 2021 *)

%o (PARI) a(n) = sum(k=1, n, gcd(k, n)^(gcd(k, n)-2));

%o (PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*d^(d-2));

%Y Cf. A000010, A342423, A342436.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Mar 12 2021