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A093888 Largest palindromic divisor of n!.

%I A093888 #33 Oct 13 2022 09:51:33
%S A093888 1,1,2,6,8,8,9,252,252,252,48384,48384,48384,48384,525525,525525,
%T A093888 525525,595595,595595,969969,969969,969969,405909504,5273993725,
%U A093888 5273993725,5273993725,5273993725,5273993725,5273993725,5273993725,5273993725,290826628092,290826628092,290826628092
%N A093888 Largest palindromic divisor of n!.
%C A093888 As positive palindromes do not end in 0 terms are not a multiple of 10. - _David A. Corneth_, Oct 07 2022
%H A093888 Michael S. Branicky, <a href="/A093888/b093888.txt">Table of n, a(n) for n = 0..60</a> (terms 1..40 from _David A. Corneth_)
%H A093888 David A. Corneth, <a href="/A093888/a093888.gp.txt">Lower bounds for a(0)..a(100)</a>
%F A093888 a(n) = A093030(A000142(n)). - _Michel Marcus_, Oct 12 2022
%e A093888 a(8) = 252 as 252 is the largest palindrome that divides 8! = 40320.
%t A093888 Table[SelectFirst[Reverse[Divisors[n!]],PalindromeQ],{n,30}] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Nov 19 2020 *)
%o A093888 (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 }
%o A093888 ispal(n) = my(d = digits(n)); d == Vecrev(d)
%o A093888 val(n, p) = my(r=0); while(n, r+=n\=p); r \\ _David A. Corneth_, Oct 07 2022
%o A093888 (Python)
%o A093888 from sympy import divisors, factorial, multiplicity
%o A093888 def ispal(n): s = str(n); return s == s[::-1]
%o A093888 def b(n, k): f = factorial(n); return f//k**multiplicity(k, f)
%o A093888 def a(n):
%o A093888     m2 = max(d for d in divisors(b(n, 2), generator=True) if ispal(d))
%o A093888     m5 = max(d for d in divisors(b(n, 5), generator=True) if ispal(d))
%o A093888     return max(m2, m5)
%o A093888 print([a(n) for n in range(34)]) # _Michael S. Branicky_, Oct 12 2022 after _David A. Corneth_
%Y A093888 Cf. A000142, A002113, A093030, A093889.
%K A093888 base,nonn
%O A093888 0,3
%A A093888 _Amarnath Murthy_, Apr 23 2004
%E A093888 More terms from _Jason Earls_, May 07 2004
%E A093888 a(0) and more terms from _David A. Corneth_, Oct 07 2022