A396228 a(1) = 1; a(n+1) = -Sum_{k=1..n} (-1)^k * a(k) * floor(n/k).

1, 1, 1, 3, 0, 1, 1, 3, -3, -4, 0, 1, -3, -5, 1, 4, -6, -11, -3, -5, 1, 5, 0, 1, -7, -13, -3, -7, 3, 7, 5, 11, -10, -18, -6, -10, 4, 9, -3, -7, 3, 7, 7, 15, -8, -16, 0, 1, -12, -22, -3, -10, 7, 15, 5, 11, 7, 13, 3, 7, -1, -1, 5, 11, -21, -44, -15, -29, 9, 20, 4, 9, 10, 21, 4, 4, -15, -28, 7, 15

Offset

1,4

Links

Table of n, a(n) for n=1..80.

Ilya Gutkovskiy, Scatterplot of the second partial sums of A396228

Formula

a(1) = 1, a(n) = -Sum_{k=1..n-1} Sum_{d|k} (-1)^d * a(d).

G.f.: x - ( x / (1 - x) ) * Sum_{n>=1} a(n) * (-x)^n / (1 - x^n).

Mathematica

a[1] = 1; a[n_] := a[n] = -Sum[(-1)^k a[k] Floor[(n - 1)/k], {k, 1, n - 1}]; Table[a[n], {n, 1, 80}]

Crossrefs

Cf. A014668, A024919, A059851, A307778, A359479, A396227.

Sequence in context: A174624 A029358 A088512 * A094921 A395047 A246522

Adjacent sequences: A396225 A396226 A396227 * A396230 A396231 A396232

Keyword

sign

Author

Ilya Gutkovskiy, May 19 2026

Status

approved