A074190 Let the index of the largest prime power that divides n! be k then the smallest number such that n!*a(n) is a perfect k-th power.

1, 1, 1, 9, 225, 1125, 385875, 446698546875, 49633171875, 1042296609375, 20311412259610828125, 9031977246542444996484375, 95779597047909624383105541891796875

Offset

1,4

Links

Table of n, a(n) for n=1..13.

Formula

If n! = 2^A*3^B*5^C*... then the largest index is A and a(n) = (2*3*5*...)^A/(n!).

Example

a(6) = 1125 as 1125*6! = 810000 = 30^4. 6! = 720 = 2^4*3^2*5 and a(6) = (2*3*5)^4/6! = 1125.

Maple

for n from 2 to 20 do f := ifactors(n!); k := f[2][1][2]:p := product(f[2][i][1]^k, i=1..nops(f[2])):a[n] := p/n!:od:1, seq(a[j], j=2..20);

Mathematica

a[1]=1; a[n_] := Module[{f}, f=FactorInteger[n! ]; (Times@@First/@f)^f[[1, 2]]/n! ]

Crossrefs

Sequence in context: A017558 A159939 A167038 * A069075 A218659 A012054

Adjacent sequences: A074187 A074188 A074189 * A074191 A074192 A074193

Keyword

nonn

Author

Amarnath Murthy, Aug 31 2002

Extensions

Corrected and extended by Sascha Kurz, Feb 01 2003

Status

approved