A348661 a(1) = 1; a(n) = Sum_{d|n, d < n} d * a(d)^(n/d).

1, 1, 1, 3, 1, 6, 1, 39, 4, 8, 1, 330, 1, 10, 9, 12495, 1, 1446, 1, 1620, 11, 14, 1, 1792050, 6, 16, 580, 10158, 1, 53002, 1, 2516534175, 15, 20, 13, 469241466, 1, 22, 17, 774558756, 1, 1696170, 1, 712914, 20160, 26, 1, 108457624531554, 8, 328588, 21, 6383964

Offset: 1

Author

Ilya Gutkovskiy, Oct 28 2021

Keywords

• nonn

Crossrefs

Cf. A006241, A008578 (positions of 1's), A157313, A165552, A196545, A281145.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = Sum[If[d < n, d a[d]^(n/d), 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 52}]

Formula

For n > 1, a(n) is the coefficient of x^n/n in expansion of -log(Product_{k=1..n-1} (1 - a(k)*x^k)).