A093889 a(n) = n!/A093888(n).

1, 1, 1, 1, 3, 15, 80, 20, 160, 1440, 75, 825, 9900, 128700, 165888, 2488320, 39813120, 597196800, 10749542400, 125411328000, 2508226560000, 52672757760000, 2769091920000, 4901791334400, 117642992025600, 2941074800640000, 76467944816640000, 2064634510049280000, 57809766281379840000, 1676483222160015360000

Offset: 0

Author

Amarnath Murthy, Apr 23 2004

Keywords

• nonn
• base

Examples

			a(4) = 3 as the largest palindromic divisor of 4! comes from the set {1, 2, 3, 4, 6, 8, 12, 24}. The largest palindrome is this set is 8 so a(4) = 4! / 8 = 3. - _David A. Corneth_, Oct 12 2022
		

Crossrefs

Cf. A000142, A093888.

Programs

Python

from sympy import divisors, factorial, multiplicity
def ispal(n): s = str(n); return s == s[::-1]
def b(f, k): return f//k**multiplicity(k, f)
def a(n):
    f = factorial(n)
    m2 = max(d for d in divisors(b(f, 2), generator=True) if ispal(d))
    m5 = max(d for d in divisors(b(f, 5), generator=True) if ispal(d))
    return f//max(m2, m5)
print([a(n) for n in range(34)]) # Michael S. Branicky, Oct 12 2022

Extensions

Corrected and extended by Jason Earls, May 07 2004

a(0) and more terms from David A. Corneth, Oct 07 2022