A180170 a(0) = 1, a(n) = n*a(n-1)*A014963(n).

1, 1, 4, 36, 288, 7200, 43200, 2116800, 33868800, 914457600, 9144576000, 1106493696000, 13277924352000, 2243969215488000, 31415569016832000, 471233535252480000, 15079473128079360000, 4357967734014935040000, 78443419212268830720000

Offset: 0

Author

R. J. Mathar, Jan 16 2011

Keywords

• nonn
• easy

Comments

Lcm of the first n terms of the sequence of the denominators A_n of the preprint.

Links

• L. A. Medina, V. H. Moll, E. S. Rowland, Iterated primitives of logarithmic powers, arXiv:0911.1325 [math.NT], 2009-2010, eq (1.6).
• Jim Pitman and Wenpin Tang, Regenerative random permutations of integers, arXiv:1704.01166, [math.PR], 2017, p. 18.

Programs

Mathematica

(* First run the program for A014963 *) b[0] := 1; b[1] := 1; b[n_] := n * b[n - 1] * a[n]; Table[b[n], {n, 0, 19}] (* Alonso del Arte, Jan 16 2011 *)
Join[{1},Table[n!LCM@@Range[n],{n,1,20}]] (* Benedict W. J. Irwin, Nov 01 2016 *)
F=Table[1,{n,1,20}];For[i=1,i<20,i++,F[[i+1]]=(i+1)*F[[i]]*Exp[MangoldtLambda[i+1]]];Join[{1},F] (* Benedict W. J. Irwin, Nov 01 2016 *)

PARI

A014963(n)=
{
    local(r);
    if( isprime(n), return(n));
    if( ispower(n,,&r) && isprime(r), return(r) );
    return(1);
}
a(n)=if(n==0,1, n * a(n-1) * A014963(n));
for(n=0,55, print1(a(n),", "))
/* Joerg Arndt, Jan 16 2011 */

Formula

a(n) = n! * lcm(1,2,...,n) = n! * A003418(n), n > 0. - Benedict W. J. Irwin, Nov 01 2016