A032512 Sum of the integer part of 4th roots of integers <= n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119

Offset: 0

Author

Michel Tixier (tixier(AT)dyadel.net)

Keywords

• nonn

Crossrefs

Cf. A022554, A031876, A032513.

Partial sums of A255270.

Programs

Mathematica

Accumulate[Floor[Surd[Range[0,70],4]]] (* Harvey P. Dale, Dec 14 2024 *)

PARI

a(n) = sum(k=1, n, sqrtnint(k, 4)); \\ Michel Marcus, Mar 12 2016

Formula

G.f.: Sum_{k>=1} x^(k^4)/(1 - x)^2. - Ilya Gutkovskiy, Dec 22 2016

a(n) = -(1/30) * floor(n^(1/4)) * (-31 - 30 * n + 10 * floor(n^(1/4))^2 + 15 * floor(n^(1/4))^3 + 6 * floor(n^(1/4))^4). - Pooya Farshim, Sep 28 2024

Extensions

NAME adapted to offset. - Giovanni Resta, May 08 2020