A396227 a(1) = 1; a(n+1) = Sum_{k=1..n} (-1)^k * a(k) * floor(n/k).

1, -1, -3, -1, -4, -1, -1, -1, -5, 2, 6, -1, -3, -1, -3, 6, 8, -1, 3, -1, 1, 3, -2, -1, -5, 3, 7, 7, 11, -1, 7, -1, 0, -4, -18, 4, 10, -1, -7, 5, 11, -1, -3, -1, -8, 14, 28, -1, 0, 0, 9, -6, -9, -1, -5, -3, -3, -1, -15, -1, 3, -1, -11, 7, 15, 6, 9, -1, -17, 4, 30, -1, 2, -1, -14, 14, 21, -6, 1, -1

Offset

1,3

Links

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

Ilya Gutkovskiy, Scatterplot of the second partial sums of A396227

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, A343370, A359479, A396228.

Sequence in context: A144211 A393288 A260510 * A125291 A320640 A055187

Adjacent sequences: A396224 A396225 A396226 * A396228 A396230 A396231

Keyword

sign

Author

Ilya Gutkovskiy, May 19 2026

Status

approved