A307793 -id:A307793 - 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

A307794 a(1) = 1; a(n+1) = Sum_{d|n} sigma(d)*a(d), where sigma = sum of divisors (A000203).

Original entry on oeis.org

1, 1, 4, 17, 123, 739, 8888, 71105, 1066698, 13867091, 249608380, 2995300561, 83868424715, 1174157946011, 28179790775372, 676314978609683, 20965764337966871, 377383758083403679, 14717966565266619443, 294359331305332388861, 12363091914824209940661, 395618941274374718172273

Offset: 1

Ilya Gutkovskiy, Apr 29 2019

nonn

Cf. A000203, A001001, A307793.

a[n_] := a[n] = Sum[DivisorSigma[1, d] a[d], {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 1, 22}]
a[n_] := a[n] = SeriesCoefficient[x (1 + Sum[DivisorSigma[1, k] a[k] x^k/(1 - x^k), {k, 1, n - 1}]), {x, 0, n}]; Table[a[n], {n, 1, 22}]

a(n) = if (n==1, 1, sumdiv(n-1, d, sigma(d)*a(d))); \\ Michel Marcus, Apr 29 2019

G.f.: x * (1 + Sum_{n>=1} sigma(n)*a(n)*x^n/(1 - x^n)).

L.g.f.: -log(Product_{i>=1, j>=1} (1 - x^(i*j))^(a(i*j)/j)) = Sum_{n>=1} a(n+1)*x^n/n.

cp's OEIS Frontend

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

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