A309633 G.f.: x * Sum_{k>=1} x^k / (1 - a(k)*x^k).

0, 1, 1, 1, 2, 1, 3, 1, 3, 2, 4, 1, 5, 1, 5, 6, 4, 1, 7, 1, 13, 11, 6, 1, 7, 17, 7, 11, 31, 1, 45, 1, 10, 18, 6, 146, 34, 1, 9, 27, 141, 1, 261, 1, 78, 364, 8, 1, 44, 730, 537, 18, 145, 1, 255, 1281, 2203, 51, 33, 1, 2213, 1, 47, 7461, 221, 4722, 1159, 1, 85, 38, 27948, 1, 2342, 1, 36, 17060, 347, 63146, 3427, 1

Offset

1,5

Links

Table of n, a(n) for n=1..80.

Formula

a(1) = 0; a(n+1) = Sum_{d|n} a(d)^(n/d-1).

Mathematica

a[n_] := a[n] = SeriesCoefficient[x Sum[x^k/(1 - a[k] x^k), {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 80}]
a[n_] := a[n] = Sum[a[d]^((n - 1)/d - 1) , {d, Divisors[n - 1]}]; a[1] = 0; a[2] = 1; Table[a[n], {n, 1, 80}]

Prog

(PARI) seq(n)={my(v=vector(n)); for(n=1, #v-1, v[n+1]=sumdiv(n, d, v[d]^(n/d-1))); v} \\ Andrew Howroyd, Aug 10 2019

Crossrefs

Cf. A028815 (positions of 1's), A087909, A127525, A309634.

Sequence in context: A331991 A351465 A309634 * A329632 A014599 A274771

Adjacent sequences: A309630 A309631 A309632 * A309634 A309635 A309636

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 10 2019

Status

approved