A345141 a(1) = 1, a(2) = 0; a(n+2) = Sum_{d|n} a(d).

1, 0, 1, 1, 2, 2, 3, 4, 4, 6, 6, 9, 7, 14, 8, 18, 12, 24, 13, 32, 14, 42, 19, 49, 20, 67, 23, 75, 29, 94, 30, 114, 31, 138, 39, 151, 45, 193, 46, 207, 55, 253, 56, 288, 57, 338, 73, 358, 74, 443, 78, 472, 92, 548, 93, 603, 102, 701, 117, 731, 118, 887, 119, 918, 142, 1056, 152, 1139, 153, 1291

Offset

1,5

Links

Table of n, a(n) for n=1..70.

Formula

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

Mathematica

a[1] = 1; a[2] = 0; a[n_] := a[n] = Sum[a[d], {d, Divisors[n - 2]}]; Table[a[n], {n, 1, 70}]
nmax = 70; A[_] = 0; Do[A[x_] = x + x^2 Sum[A[x^k], {k, 1, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest

Crossrefs

Cf. A003238, A007439, A345137, A345138.

Sequence in context: A138374 A029936 A114093 * A239950 A077768 A143038

Adjacent sequences: A345138 A345139 A345140 * A345142 A345143 A345144

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 09 2021

Status

approved