A363838 a(n) = Product_{b=2..n} b^gamma(n, b) where gamma(n, b) = Sum_{i>=1} floor(n/b^i).

1, 1, 2, 6, 96, 480, 17280, 120960, 30965760, 2508226560, 250822656000, 2759049216000, 9535274090496000, 123958563176448000, 24295878382583808000, 5466572636081356800000, 179128652139113899622400000, 3045187086364936293580800000, 53278593263040925392489676800000

Offset: 0

Author

Michel Marcus, Oct 20 2023

Keywords

• nonn

Comments

Generalized factorials.

Links

• Michel Marcus, Table of n, a(n) for n = 0..100
• Jeffrey C. Lagarias and Wijit Yangjit, The factorial function and generalizations, extended, arXiv:2310.12949 [math.NT], 2023. See Section 7.2 p. 20 and Table 2 p. 29.

Crossrefs

Row products of A153216.

Programs

PARI

f(n, b) = sum(i=1, logint(n, b), n\b^i);
a(n) = prod(b=2, n, b^f(n,b));

Python

from math import prod
from sympy import integer_log
def A363838(n): return prod(b**sum(n//b**i for i in range(1,integer_log(n,b)[0]+1)) for b in range(2,n+1)) # Chai Wah Wu, Oct 20 2023