A225558 a(n) = A003418(n)/A000793(n).

1, 1, 1, 2, 3, 10, 10, 35, 56, 126, 84, 924, 462, 6006, 4290, 3432, 5148, 58344, 58344, 554268, 554268, 554268, 554268, 6374082, 6374082, 21246940, 21246940, 52151580, 34767720, 924241890, 504131940, 15628090140, 26447537160, 26447537160, 15628090140

Offset: 0

Author

Antti Karttunen, May 10 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000793, A003418.

Programs

Maple

g:= proc(n) g(n):= `if`(n=0, 1, ilcm(n, g(n-1))) end:
b:= proc(n, i) option remember; local p;
      p:= `if`(i<1, 1, ithprime(i));
      `if`(n=0 or i<1, 1, max(b(n, i-1),
           seq(p^j*b(n-p^j, i-1), j=1..ilog[p](n))))
    end:
a:= n->g(n)/b(n, `if`(n<8, 3,
    numtheory[pi](ceil(1.328*isqrt(n*ilog(n)))))):
seq(a(n), n=0..40); # Alois P. Heinz, May 22 2013

Mathematica

b[n_, i_] := b[n, i] = Module[{p}, p = If[i<1, 1, Prime[i]]; If[n==0 || i<1, 1, Max[b[n, i-1], Table[p^j*b[n-p^j, i-1], {j, 1, Log[p, n] // Floor }]]]]; a[0]=1; a[n_] := LCM @@ Range[n] / b[n, If[n<8, 3, PrimePi[ Ceiling[ 1.328*Sqrt[n*Log[n] // Floor]]]]]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 27 2016, after Alois P. Heinz *)

Formula

a(n) = A003418(n)/A000793(n).

A074115(n)/a(n) = A025527(n).