A309286 a(0) = 0, a(1) = 1, and for any n > 1, a(n) = Sum_{k > 1} (-1)^k * a(floor(n/k^2)).

0, 1, 0, 0, 1, 1, 1, 1, 0, -1, -1, -1, -1, -1, -1, -1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -3, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3

Offset

0,19

Comments

This sequence is a signed variant of A309262.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Example

a(9) = a(floor(9/2^2)) - a(floor(9/3^3)) = a(2) - a(1) = 0 - 1 = -1.

Mathematica

Join[{0}, Clear[a]; a[0]=0; a[1]=1; a[n_]:=a[n]=Sum[a[Floor[n/k^2]](-1)^k, {k, 2, n}]; Table[a[n], {n, 1, 100}]] (* Vincenzo Librandi, Jul 22 2019 *)

Prog

(PARI) a(n) = if (n<=1, n, sum (k=2, sqrtint(n), (-1)^k * a(n\k^2)))

Crossrefs

Cf. A309262.

Sequence in context: A044925 A323356 A319244 * A102671 A292519 A037815

Adjacent sequences: A309283 A309284 A309285 * A309287 A309288 A309289

Keyword

sign

Author

Rémy Sigrist, Jul 21 2019

Status

approved