A099946 a(n) = lcm{1, 2, ..., n}/(n*(n-1)), n >= 2.

1, 1, 1, 3, 2, 10, 15, 35, 28, 252, 210, 2310, 1980, 1716, 3003, 45045, 40040, 680680, 612612, 554268, 503880, 10581480, 9699690, 44618574, 41186376, 114406600, 106234700, 2868336900, 2677114440, 77636318760, 145568097675, 136745788725

Offset: 2

Author

N. J. A. Sloane, Nov 12 2004

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..1000 (first 99 terms from Luke March)

Crossrefs

Cf. A002378, A002944, A003418, A025558.

Programs

Maple

a:= n-> ilcm(seq(k,k=1..n))/n/(n-1): seq(a(n), n=2..37); # Emeric Deutsch, Jun 13 2005

Mathematica

Table[LCM@@Range[n]/(n(n-1)), {n,2,40}] (* Harvey P. Dale, Jan 14 2011 *)

PARI

a(n) = lcm(vector(n, i, i))/(n*(n-1)); \\ Michel Marcus, Jul 25 2014

Python

from math import gcd
def lcm(a, b):
    return (a * b) // gcd(a, b)
def f(lim):
    l = 1
    for n in range(2, lim + 1):
        l = lcm(n, l)
        print(n, l // (n * (n - 1)))
f(100) # Luke March, Jul 23 2014

Formula

a(n) = A003418(n)/(n*(n-1)) = A003418(n)/A002378(n-1), n >= 2.

Extensions

More terms from Emeric Deutsch, Jun 13 2005