A350222 a(n) = Sum_{k=1..n} (-1)^(k+1) * floor((n/k)^3).

1, 7, 25, 57, 114, 194, 310, 460, 658, 902, 1200, 1557, 1981, 2474, 3045, 3690, 4431, 5257, 6186, 7212, 8350, 9601, 10969, 12461, 14088, 15844, 17746, 19791, 21990, 24343, 26859, 29539, 32399, 35434, 38655, 42060, 45671, 49468, 53480, 57698, 62137, 66793, 71681

Offset

1,2

Links

Table of n, a(n) for n=1..43.

Formula

a(n) = A309082(n^3).

Mathematica

a[n_] := Sum[(-1)^(k + 1)*Floor[(n/k)^3], {k, 1, n}]; Array[a, 50] (* Amiram Eldar, Dec 20 2021 *)

Prog

(PARI) a(n) = sum(k=1, n, (-1)^(k+1)*(n^3\k^3));
(Python)
def A350222(n): return (m:=n**3)+sum(m//k**3 if k&1 else -(m//k**3) for k in range(2, n+1)) # Chai Wah Wu, Oct 27 2023

Crossrefs

Cf. A000578, A309082, A344675, A344721, A350221, A350224.

Sequence in context: A155261 A365444 A268239 * A110672 A213481 A266709

Adjacent sequences: A350219 A350220 A350221 * A350223 A350224 A350225

Keyword

nonn

Author

Seiichi Manyama, Dec 20 2021

Status

approved