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

Author

Michel Tixier (tixier(AT)dyadel.net)

Keywords

• nonn

Crossrefs

Cf. A022554, A031876, A032512.

Partial sums of A178487.

Programs

Mathematica

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

PARI

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

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