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A363499
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a(n) = Sum_{k=0..n} floor(sqrt(k))^5.
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4
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0, 1, 2, 3, 35, 67, 99, 131, 163, 406, 649, 892, 1135, 1378, 1621, 1864, 2888, 3912, 4936, 5960, 6984, 8008, 9032, 10056, 11080, 14205, 17330, 20455, 23580, 26705, 29830, 32955, 36080, 39205, 42330, 45455, 53231, 61007, 68783, 76559, 84335, 92111, 99887
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OFFSET
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0,3
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COMMENTS
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Partial sums of the fifth powers of the terms of A000196.
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LINKS
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FORMULA
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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)).
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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