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a(1) = 1; a(n+1) = Sum_{d|n} phi(d) * a(d).
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%I #11 May 09 2021 08:06:51

%S 1,1,2,5,12,49,104,625,2512,15077,60358,603581,2414438,28973257,

%T 173840168,1390721397,11125773688,178012379009,1068074289230,

%U 19225337206141,153802697709496,1845632372514581,18456323725749392,406039121966486625,3248312975734309938

%N a(1) = 1; a(n+1) = Sum_{d|n} phi(d) * a(d).

%H Vaclav Kotesovec, <a href="/A332791/b332791.txt">Table of n, a(n) for n = 1..495</a>

%F a(1) = 1; a(n+1) = Sum_{k=1..n} a(n/gcd(n, k)).

%F a(n) = Sum_{k=1..n} a(gcd(n,k))*phi(gcd(n,k))/phi(n/gcd(n,k)). - _Richard L. Ollerton_, May 07 2021

%t a[1] = 1; a[n_] := Sum[EulerPhi[d] a[d], {d, Divisors[n - 1]}]; Table[a[n], {n, 1, 25}]

%t a[1] = 1; a[n_] := a[n] = Sum[a[(n - 1)/GCD[n - 1, k]], {k, 1, n - 1}]; Table[a[n], {n, 1, 25}]

%Y Cf. A000010, A006874, A038045, A057660, A307793, A307794, A332792.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, Feb 24 2020