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A049413
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Largest prime dividing Sum_{k=0..n} k! * (n-k)!.
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1
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2, 5, 2, 2, 13, 151, 3, 83, 73, 1433, 647, 29, 28211, 337, 19, 73, 18181, 130349, 771079, 731957, 6619, 4111, 61927, 140001721, 42829, 774885169, 745984697, 41711914513, 34311919, 117695654963, 1139908799, 2390249, 54413, 4707207067, 129164452987, 12496027
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OFFSET
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1,1
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COMMENTS
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Sum_{k=0..n} k! * (n-k)! = (n+1)! * Sum_{k=0..n} 1 / ((k+1) * 2^(n-k)).
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LINKS
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EXAMPLE
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a(5)=13 because Sum_{k=0..5} k! * (5-k)! = 312 = 2^3*3*13.
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MAPLE
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for n from 1 to 33 do s := 0:for k from 0 to n do s := s+k!*(n-k)!:od: ifactor(s); od;
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MATHEMATICA
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Table[FactorInteger[Sum[k!(n-k)!, {k, 0, n}]][[-1, 1]], {n, 40}] (* Harvey P. Dale, May 23 2015 *)
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PROG
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(PARI) a(n) = my(f = factor(sum(k=0, n, k!*(n-k)!))); f[#f~, 1]; \\ Michel Marcus, May 18 2014
(Python)
from sympy import factorial as f, primefactors
def a(n): return max(primefactors(sum(f(k)*f(n-k) for k in range(n+1))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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More terms from Andrew Gacek (andrew(AT)dgi.net), Apr 21 2000
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STATUS
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approved
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