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A180170 a(0) = 1, a(n) = n*a(n-1)*A014963(n). 0
1, 1, 4, 36, 288, 7200, 43200, 2116800, 33868800, 914457600, 9144576000, 1106493696000, 13277924352000, 2243969215488000, 31415569016832000, 471233535252480000, 15079473128079360000, 4357967734014935040000, 78443419212268830720000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

Table of n, a(n) for n=0..18.

L. A. Medina, V. H. Moll, E. S. Rowland, Iterated primitives of logarithmic powers, arXiv:0911.1325 [math.NT], 2009, eq (1.6)

FORMULA

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

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 *)

PROG

(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 */

CROSSREFS

Sequence in context: A173429 A172134 A098916 * A277174 A059416 A240889

Adjacent sequences:  A180167 A180168 A180169 * A180171 A180172 A180173

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, Jan 16 2011

STATUS

approved

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Last modified September 22 09:19 EDT 2017. Contains 292336 sequences.