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A049413 Highest prime dividing sum{k=0 to n}[ k!(n-k)! ]. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

sum{k=0 to n}[ k!(n-k)! ]=(n+1)!sum{k=0 to n}[ 1/((k+1)2^(n-k)) ]

LINKS

Robert Israel, Table of n, a(n) for n = 1..167

EXAMPLE

a(5)=13 because sum{k=0 to 5}[ k!(5-k)! ]=312=2^3*3*13.

MAPLE

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;

MATHEMATICA

Table[FactorInteger[Sum[k!(n-k)!, {k, 0, n}]][[-1, 1]], {n, 40}] (* Harvey P. Dale, May 23 2015 *)

PROG

(PARI) a(n) = my(f = factor(sum(k=0, n, k!*(n-k)!))); f[#f~, 1]; \\ Michel Marcus, May 18 2014

CROSSREFS

Sequence in context: A273990 A216022 A100955 * A300691 A102707 A134486

Adjacent sequences:  A049410 A049411 A049412 * A049414 A049415 A049416

KEYWORD

nonn,easy

AUTHOR

Leroy Quet

EXTENSIONS

More terms from Andrew Gacek (andrew(AT)dgi.net), Apr 21 2000

Corrected by Jud McCranie, Jan 03 2001

a(34)-a(36) from Michel Marcus, May 18 2014

STATUS

approved

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Last modified September 19 15:24 EDT 2019. Contains 327198 sequences. (Running on oeis4.)