A373048 Number of squares between n! and (n+1)!, exclusive.

0, 0, 1, 2, 6, 16, 44, 130, 402, 1302, 4413, 15569, 57025, 216348, 848276, 3430608, 14285534, 61155157, 268761742, 1210999692, 5588016550, 26378327264, 127259503463, 626899847777, 3150741885292, 16143690587631, 84267627864828, 447817207758155, 2421343092445682

Offset

0,4

Comments

Number of integers k such that n! < k^2 < (n + 1)!.

Links

Table of n, a(n) for n=0..28.

Formula

a(n) = A055226(n+1) - A055226(n). - Alois P. Heinz, Aug 02 2024

Example

For n = 3, between 3! and 4! there are only two squares: 9 and 16, so a(3) = 2.

Prog

(Python)
from math import isqrt, factorial
def A373048(n): return isqrt((m:=factorial(n))*(n+1))-isqrt(m) # Chai Wah Wu, Aug 03 2024

Crossrefs

Cf. A000142, A000290, A055226.

Sequence in context: A026134 A105696 A074413 * A263897 A209629 A349488

Adjacent sequences: A373045 A373046 A373047 * A373049 A373050 A373051

Keyword

nonn,easy

Author

Gonzalo Martínez, Aug 02 2024

Status

approved