A343371 a(n) = 1 + Sum_{d|n, d < n} a(d - 1).

1, 1, 2, 2, 3, 2, 5, 2, 5, 4, 6, 2, 9, 2, 8, 7, 7, 2, 12, 2, 12, 9, 9, 2, 13, 5, 12, 9, 12, 2, 22, 2, 14, 10, 10, 10, 18, 2, 15, 13, 16, 2, 26, 2, 20, 20, 12, 2, 22, 7, 23, 11, 19, 2, 26, 11, 23, 16, 15, 2, 30, 2, 25, 26, 16, 14, 36, 2, 22, 13, 27, 2, 32, 2, 21, 28

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

G.f. A(x) satisfies: A(x) = 1 / (1 - x) + x^2 * A(x^2) + x^3 * A(x^3) + x^4 * A(x^4) + ...

Maple

a:= proc(n) option remember;
      1+add(a(d-1), d=numtheory[divisors](n) minus {n})
    end:
seq(a(n), n=0..75);  # Alois P. Heinz, Apr 12 2021

Mathematica

a[n_] := a[n] = 1 + Sum[If[d < n, a[d - 1], 0], {d, Divisors[n]}]; Table[a[n], {n, 0, 75}]
nmax = 75; A[_] = 0; Do[A[x_] = 1/(1 - x) + Sum[x^k A[x^k], {k, 2, nmax}] + O[x]^(nmax + 1) //Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A003238, A067824, A068336, A167865.

Sequence in context: A322900 A238791 A007012 * A298423 A319810 A325250

Adjacent sequences: A343368 A343369 A343370 * A343372 A343373 A343374

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 12 2021

Status

approved