OFFSET
0,4
COMMENTS
"Strictly between" in the name means n^2 and n^3 are excluded.
If n^2 and n^3 are included we get A349993.
LINKS
Karl-Heinz Hofmann, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = floor(n^(3/2)) - n - [n>1 and A010052(n)=1]. - Giorgos Kalogeropoulos, Dec 08 2021
For n > 1, a(n) = floor(sqrt(n^3-1)) - n. - Chai Wah Wu, Dec 08 2021
MATHEMATICA
Join[{0, 0}, Table[Floor[s=n^(3/2)]-n-Boole@IntegerQ@s, {n, 2, 100}]] (* Giorgos Kalogeropoulos, Dec 08 2021 *)
PROG
(PARI) for(n=0, 58, my(n2=n^2+1, n3=n^3-1); print1(sum(k=n2, n3, issquare(k)), ", "))
(Python)
def a(n):
counter = 1
while (n+counter)**2 < n**3:
counter += 1
return (counter-1)
print([a(n) for n in range(0, 10001)])
(Python)
from math import isqrt
def A349662(n): return 0 if n <= 1 else isqrt(n**3-1) - n # Chai Wah Wu, Dec 08 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Karl-Heinz Hofmann, Dec 07 2021
STATUS
approved