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A093888
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Largest palindromic divisor of n!.
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5
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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
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0,3
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COMMENTS
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As positive palindromes do not end in 0 terms are not a multiple of 10. - David A. Corneth, Oct 07 2022
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LINKS
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FORMULA
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EXAMPLE
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a(8) = 252 as 252 is the largest palindrome that divides 8! = 40320.
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MATHEMATICA
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Table[SelectFirst[Reverse[Divisors[n!]], PalindromeQ], {n, 30}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 19 2020 *)
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PROG
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(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)
(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)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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