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

%I A180170 #31 Mar 13 2018 04:14:43
%S A180170 1,1,4,36,288,7200,43200,2116800,33868800,914457600,9144576000,
%T A180170 1106493696000,13277924352000,2243969215488000,31415569016832000,
%U A180170 471233535252480000,15079473128079360000,4357967734014935040000,78443419212268830720000
%N A180170 a(0) = 1, a(n) = n*a(n-1)*A014963(n).
%C A180170 Lcm of the first n terms of the sequence of the denominators A_n of the preprint.
%H A180170 L. A. Medina, V. H. Moll, E. S. Rowland, <a href="https://arxiv.org/abs/0911.1325">Iterated primitives of logarithmic powers</a>, arXiv:0911.1325 [math.NT], 2009-2010, eq (1.6).
%H A180170 Jim Pitman and Wenpin Tang, <a href="https://arxiv.org/abs/1704.01166">Regenerative random permutations of integers</a>, arXiv:1704.01166, [math.PR], 2017, p. 18.
%F A180170 a(n) = n! * lcm(1,2,...,n) = n! * A003418(n), n > 0. - _Benedict W. J. Irwin_, Nov 01 2016
%t A180170 (* 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 *)
%t A180170 Join[{1},Table[n!LCM@@Range[n],{n,1,20}]] (* _Benedict W. J. Irwin_, Nov 01 2016 *)
%t A180170 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 *)
%o A180170 (PARI)
%o A180170 A014963(n)=
%o A180170 {
%o A180170     local(r);
%o A180170     if( isprime(n), return(n));
%o A180170     if( ispower(n,,&r) && isprime(r), return(r) );
%o A180170     return(1);
%o A180170 }
%o A180170 a(n)=if(n==0,1, n * a(n-1) * A014963(n));
%o A180170 for(n=0,55, print1(a(n),", "))
%o A180170 /* _Joerg Arndt_, Jan 16 2011 */
%K A180170 nonn,easy
%O A180170 0,3
%A A180170 _R. J. Mathar_, Jan 16 2011