A350239 a(n) = Sum_{k=1..n} (-1)^(k+1) * floor((n/(2*k))^k).

0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 0, 0, 2, 2, 2, 2, 3, 1, 0, 1, 3, 2, 2, 1, 4, -1, -1, 2, 2, 2, 1, 2, 1, 1, 0, 2, 3, 1, 2, 0, 2, 0, -2, 1, 2, 2, -1, 2, 2, -2, 2, 1, 2, 2, -1, 0, 3, 3, -1, -1, 7, 2, 2, 1, 2, 0, 0, -2, 3, 1, 2, -2, 4, -3, -2, -2, 3, 1, -1, 0, 1, 2, 1, 1, 0, 2, 3, 1, 5, 2, -1, 2, 4, 1, 1, 0, 1, 1

Offset

1,6

Links

Seiichi Manyama, Table of n, a(n) for n = 1..5000

Example

a(3) = [3/2]  = 1.
a(4) = [4/2] - [(4/4)^2] = 2 - 1 = 1.
a(5) = [5/2] - [(5/4)^2] = 2 - 1 = 1.

Mathematica

a[n_] := Sum[(-1)^(k + 1)*Floor[(n/(2*k))^k], {k, 1, n}]; Array[a, 100] (* Amiram Eldar, Dec 21 2021 *)

Prog

(PARI) a(n) = sum(k=1, n\2, (-1)^(k+1)*(n^k\(2*k)^k));

Crossrefs

Cf. A350223, A350238.

Sequence in context: A187759 A358565 A270645 * A268059 A037226 A089641

Adjacent sequences: A350236 A350237 A350238 * A350240 A350241 A350242

Keyword

sign

Author

Seiichi Manyama, Dec 21 2021

Status

approved