A346117 a(1) = a(2) = 1; a(n+2) = 1 + Sum_{d|n} a(d).

1, 1, 2, 3, 4, 6, 6, 11, 8, 17, 12, 24, 14, 38, 16, 47, 24, 64, 26, 83, 28, 110, 38, 125, 40, 174, 46, 191, 58, 241, 60, 289, 62, 353, 78, 380, 90, 490, 92, 519, 110, 640, 112, 723, 114, 851, 146, 892, 148, 1113, 156, 1177, 184, 1371, 186, 1500, 204, 1752, 234, 1813

Offset

1,3

Links

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

Formula

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

Maple

f:= proc(n) option remember; local d; 1 + add(procname(d), d = numtheory:-divisors(n-2)) end proc:
f(1):= 1: f(2):= 1:
map(f, [$1..60]); # Robert Israel, Dec 02 2022

Mathematica

a[1] = a[2] = 1; a[n_] := a[n] = 1 + Sum[a[d], {d, Divisors[n - 2]}]; Table[a[n], {n, 1, 60}]
nmax = 60; A[_] = 0; Do[A[x_] = x + x^2 (1/(1 - x) + Sum[A[x^k], {k, 1, nmax}]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest

Crossrefs

Cf. A007439, A068336.

Sequence in context: A332295 A332576 A028335 * A007464 A210733 A265564

Adjacent sequences: A346114 A346115 A346116 * A346118 A346119 A346120

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 05 2021

Status

approved