A349993 a(n) is the number of squares k^2 with n^2 <= k^2 <= n^3.

1, 1, 1, 3, 5, 7, 9, 12, 15, 19, 22, 26, 30, 34, 39, 44, 49, 54, 59, 64, 70, 76, 82, 88, 94, 101, 107, 114, 121, 128, 135, 142, 150, 157, 165, 173, 181, 189, 197, 205, 213, 222, 231, 239, 248, 257, 266, 276, 285, 295, 304, 314, 323, 333, 343, 353, 364, 374, 384, 395, 405

Offset

0,4

Comments

Interval with n^2 and n^3 excluded is A349662.

Links

Karl-Heinz Hofmann, Table of n, a(n) for n = 0..10000

Formula

a(n) = floor(sqrt(n^3)) - n + 1. - Giorgos Kalogeropoulos, Dec 08 2021

Mathematica

Table[Floor[Sqrt[n^3]]-n+1, {n, 0, 100}] (* Giorgos Kalogeropoulos, Dec 08 2021 *)

Prog

(PARI) a(n) = sqrtint(n^3) - n + 1
(PARI) a(n)=sum(k=n^2, n^3, issquare(k))
(PARI) for(n=0, 60, my(n2=n^2, n3=n^3); print1(sum(k=n2, n3, issquare(k)), ", "))
(Python)
def a(n):
    counter = 0
    while (n+counter)**2 <= n**3: counter += 1
    return (counter)
print([a(n) for n in range(0, 60)])
(Python)
from math import isqrt
def A349993(n): return isqrt(n**3) - n + 1 # Chai Wah Wu, Dec 08 2021

Crossrefs

Cf. A000290, A000578.

Cf. A349662 (number of squares k^2 with n^2 < k^2 < n^3).

Cf. A028387 (Also the number of squares between (n+2)^2 and (n+2)^4).

Sequence in context: A080751 A025218 A258782 * A007078 A226332 A226331

Adjacent sequences: A349990 A349991 A349992 * A349994 A349995 A349996

Keyword

nonn,easy

Author

Karl-Heinz Hofmann and Hugo Pfoertner, Dec 08 2021

Status

approved