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A373048
Number of squares between n! and (n+1)!, exclusive.
1
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)!.
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
KEYWORD
nonn,easy
AUTHOR
Gonzalo Martínez, Aug 02 2024
STATUS
approved