A135354 a(0)=1, a(n) = largest divisor of n! that is coprime to a(n-1).

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

Offset: 0

Author

Leroy Quet, Dec 07 2007

Keywords

• nonn
• look

Links

• Robert Israel, Table of n, a(n) for n = 0..504

Crossrefs

Cf. A060818, A049606.

Programs

Maple

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:
R; # Robert Israel, Jul 21 2024

Mathematica

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 *)

Formula

a(2n) = the largest power of 2 that divides (2n)!. a(2n+1) = the largest odd divisor of (2n+1)! = (2n+1)!/a(2n).

Extensions

More terms from Stefan Steinerberger, Dec 10 2007

More terms from Robert Israel, Jul 21 2024