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A032513
Sum of the integer part of 5th roots of positive integers less than or equal to n.
6
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
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
Partial sums of A178487.
Sequence in context: A373868 A166718 A132016 * A272323 A273881 A048266
KEYWORD
nonn
AUTHOR
Michel Tixier (tixier(AT)dyadel.net)
STATUS
approved