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A135354
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a(0)=1, a(n) = largest divisor of n! that is coprime to a(n-1).
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1
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1, 1, 2, 3, 8, 15, 16, 315, 128, 2835, 256, 155925, 1024, 6081075, 2048, 638512875, 32768, 10854718875, 65536, 1856156927625, 262144, 194896477400625, 524288, 49308808782358125, 4194304, 3698160658676859375, 8388608, 1298054391195577640625, 33554432, 263505041412702261046875, 67108864
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OFFSET
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0,3
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LINKS
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FORMULA
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a(2n) = the largest power of 2 that divides (2n)!. a(2n+1) = the largest odd divisor of (2n+1)! = (2n+1)!/a(2n).
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MAPLE
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f:= proc(n, a)
local P, R, i;
P:= select(t -> isprime(t) and igcd(t, a)=1, [2, seq(i, i=3..n, 2)]);
R:= map(proc(p) local k; add(floor(n/p^k), k=1 ..ilog[p](n)) end proc, P);
mul(P[i]^R[i], i=1..nops(P));
end proc:
R:= 1: r:= 1: for i from 1 to 50 do r:= f(i, r); R:= R, r od:
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MATHEMATICA
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a = {1}; For[n = 1, n < 25, n++, AppendTo[a, Select[Divisors[n! ], GCD[a[[ -1]], # ] == 1 &][[ -1]]]]; a (* Stefan Steinerberger, Dec 10 2007 *)
ldnf[{n_, a_}]:={n+1, Max[Select[Divisors[(n+1)!], CoprimeQ[#, a]&]]}; Transpose[ NestList[ldnf, {0, 1}, 30]][[2]] (* Harvey P. Dale, Jan 21 2016 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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