OFFSET
0,3
COMMENTS
Partial sums of the fifth powers of the terms of A000196.
LINKS
Karl-Heinz Hofmann, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = (n+1)*m^5 - (1/84)*m*(m+1)*(2*m+1)*(3*m-1)*(10*m^3-7*m+4), where m = floor(sqrt(n)).
MATHEMATICA
Table[(n + 1) #^5 - (1/84) # (# + 1)*(2 # + 1)*(3 # - 1)*(10 #^3 - 7 # + 4) &[Floor@ Sqrt[n]], {n, 0, 42}] (* Michael De Vlieger, Jun 10 2023 *)
PROG
(Python)
from math import isqrt
def A363499(n): return (m:=isqrt(n))**5 *(n+1) - (m*(m+1)*(2*m+1)*(3*m-1)*(10*m**3-7*m+4))//84 # Karl-Heinz Hofmann, Jul 17 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Hans J. H. Tuenter, Jun 05 2023
STATUS
approved