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Sum of the integer part of 4th roots of integers <= n.
6

%I #27 Dec 14 2024 16:30:12

%S 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,

%T 37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,

%U 83,85,87,89,91,93,95,97,99,101,103,105,107,109,111,113,115,117,119

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

%F G.f.: Sum_{k>=1} x^(k^4)/(1 - x)^2. - _Ilya Gutkovskiy_, Dec 22 2016

%F 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

%t Accumulate[Floor[Surd[Range[0,70],4]]] (* _Harvey P. Dale_, Dec 14 2024 *)

%o (PARI) a(n) = sum(k=1, n, sqrtnint(k, 4)); \\ _Michel Marcus_, Mar 12 2016

%Y Cf. A022554, A031876, A032513.

%Y Partial sums of A255270.

%K nonn

%O 0,3

%A Michel Tixier (tixier(AT)dyadel.net)

%E NAME adapted to offset. - _Giovanni Resta_, May 08 2020