A332792 -id:A332792 - cp's OEIS frontend

A332791 a(1) = 1; a(n+1) = Sum_{d|n} phi(d) * a(d).

1, 1, 2, 5, 12, 49, 104, 625, 2512, 15077, 60358, 603581, 2414438, 28973257, 173840168, 1390721397, 11125773688, 178012379009, 1068074289230, 19225337206141, 153802697709496, 1845632372514581, 18456323725749392, 406039121966486625, 3248312975734309938

Offset: 1

Ilya Gutkovskiy, Feb 24 2020

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 1..495

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

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

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

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

A343761 a(1) = 1; a(n) = -Sum_{k=1..n, gcd(n,k) > 1} a(n/gcd(n,k)).

Original entry on oeis.org

1, -1, -1, 0, -1, 2, -1, 0, 1, 4, -1, -2, -1, 6, 5, 0, -1, -8, -1, -12, 7, 10, -1, 6, 3, 12, -5, -30, -1, -54, -1, 0, 11, 16, 9, 48, -1, 18, 13, 84, -1, -116, -1, -90, -41, 22, -1, -42, 5, -72, 17, -132, -1, 130, 13, 330, 19, 28, -1, 482, -1, 30, -83, 0, 15, -312, -1, -240, 23, -258

Offset: 1

Ilya Gutkovskiy, Apr 28 2021

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000010, A023900, A054531, A332792, A343762.

f:= proc(n) option remember; local G,g;
  G:= subs(1=NULL, map(igcd,[$1..n],n));
  -add(procname(n/g), g=G);
end proc:
f(1):= 1:
map(f, [$1..100]); # Robert Israel, Dec 21 2022

a[1] = 1; a[n_] := a[n] = -Sum[If[GCD[n, k] > 1, a[n/GCD[n, k]], 0], {k, 1, n}]; Table[a[n], {n, 1, 70}]
a[1] = 1; a[n_] := -Sum[If[d < n, EulerPhi[d] a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 70}]

a(1) = 1; a(n) = -Sum_{d|n, d < n} phi(d) * a(d).

cp's OEIS Frontend

A332791 a(1) = 1; a(n+1) = Sum_{d|n} phi(d) * a(d).

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