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A093888

Largest palindromic divisor of n!.

1, 1, 2, 6, 8, 8, 9, 252, 252, 252, 48384, 48384, 48384, 48384, 525525, 525525, 525525, 595595, 595595, 969969, 969969, 969969, 405909504, 5273993725, 5273993725, 5273993725, 5273993725, 5273993725, 5273993725, 5273993725, 5273993725, 290826628092, 290826628092, 290826628092

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OFFSET

0,3

COMMENTS

As positive palindromes do not end in 0 terms are not a multiple of 10. - David A. Corneth, Oct 07 2022

LINKS

Michael S. Branicky, Table of n, a(n) for n = 0..60 (terms 1..40 from David A. Corneth)

David A. Corneth, Lower bounds for a(0)..a(100)

FORMULA

a(n) = A093030(A000142(n)). - Michel Marcus, Oct 12 2022

EXAMPLE

a(8) = 252 as 252 is the largest palindrome that divides 8! = 40320.

MATHEMATICA

Table[SelectFirst[Reverse[Divisors[n!]], PalindromeQ], {n, 30}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 19 2020 *)

PROG

(PARI) a(n) = { res = 1; my(d = divisors(n! >> val(n, 2))); forstep(i = #d, 1, -1, if(ispal(d[i]), res = d[i]; break; ) ); d = divisors(n! / 5^val(n, 5)); forstep(i = #d, 1, -1, if(d[i] < res, return(res); ); if(ispal(d[i]), res = d[i]; break; ) ); res }

ispal(n) = my(d = digits(n)); d == Vecrev(d)

val(n, p) = my(r=0); while(n, r+=n\=p); r \\ David A. Corneth, Oct 07 2022

(Python)

from sympy import divisors, factorial, multiplicity

def ispal(n): s = str(n); return s == s[::-1]

def b(n, k): f = factorial(n); return f//k**multiplicity(k, f)

def a(n):

m2 = max(d for d in divisors(b(n, 2), generator=True) if ispal(d))

m5 = max(d for d in divisors(b(n, 5), generator=True) if ispal(d))

return max(m2, m5)

print([a(n) for n in range(34)]) # Michael S. Branicky, Oct 12 2022 after David A. Corneth

CROSSREFS