A032513 Sum of the integer part of 5th roots of positive integers less than or equal to n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 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

Offset

0,3

Links

Table of n, a(n) for n=0..69.

Formula

G.f.: Sum_{k>=1} x^(k^5)/(1 - x)^2. - Ilya Gutkovskiy, Dec 22 2016

a(n) = -(1/12) * floor(n^(1/5)) * (-12 - 12*n - floor(n^(1/5)) + 5*floor(n^(1/5))^3 + 6*floor(n^(1/5))^4 + 2*floor(n^(1/5))^5). - Pooya Farshim, Sep 28 2024

Mathematica

Accumulate[Floor[Surd[Range[0, 70], 5]]] (* Harvey P. Dale, Jan 21 2019 *)

Prog

(PARI) a(n) = sum(k=1, n, sqrtnint(k, 5)); \\ Michel Marcus, Mar 12 2016

Crossrefs

Cf. A022554, A031876, A032512.

Partial sums of A178487.

Sequence in context: A373868 A166718 A132016 * A272323 A273881 A048266

Adjacent sequences: A032510 A032511 A032512 * A032514 A032515 A032516

Keyword

nonn

Author

Michel Tixier (tixier(AT)dyadel.net)

Status

approved