A345182 a(1) = 1, a(2) = 0; a(n) = Sum_{d|n, d < n} a(d).

1, 0, 1, 1, 1, 2, 1, 2, 2, 2, 1, 5, 1, 2, 3, 4, 1, 6, 1, 5, 3, 2, 1, 12, 2, 2, 4, 5, 1, 10, 1, 8, 3, 2, 3, 18, 1, 2, 3, 12, 1, 10, 1, 5, 8, 2, 1, 28, 2, 6, 3, 5, 1, 16, 3, 12, 3, 2, 1, 31, 1, 2, 8, 16, 3, 10, 1, 5, 3, 10, 1, 50, 1, 2, 8, 5, 3, 10, 1, 28, 8, 2, 1, 31, 3, 2, 3, 12, 1, 36

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

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

a(n) = A074206(n) if n is odd, otherwise a(n) = A074206(n) - A074206(n/2).

Mathematica

a[1] = 1; a[2] = 0; a[n_] := a[n] = Sum[If[d < n, a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 90}]
nmax = 90; A[_] = 0; Do[A[x_] = x - x^2 + Sum[A[x^k], {k, 2, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest

Crossrefs

Cf. A022825 (partial sums), A074206, A167865, A320224, A345138, A345141.

Sequence in context: A324114 A011776 A375624 * A297791 A098965 A290087

Adjacent sequences: A345179 A345180 A345181 * A345183 A345184 A345185

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 10 2021

Status

approved