A085081 Group the natural numbers such that the product of the terms of the n-th group has a divisor with the same prime signature as that of the product of the terms of the (n-1)-th group. (1), (2), (3), (4), (5,6,7,8), (9,10,11,12,13,14),... Sequence contains the product of the terms of the groups.

1, 2, 3, 4, 1680, 2162160, 586051200, 5967561600, 1220096908800, 33371339479827148800, 10221346459144248675287040000, 1065516759202418135010355181075171069914644480000000

Offset

1,2

Comments

In most cases when n >3 a(n) is a multiple of a(n-1). Question: is it true for all n >3.

For 6 <= n <= 13, a(n) doesn't divide a(n+1). I believe this also holds for all larger n. - David Wasserman, Jan 18 2005

Links

Table of n, a(n) for n=1..12.

Example

a(5) = 2162160 = 2^4*3^3*5*7*11*13 and a(4) = 1680= 2^4*3*5*7.
a(4) itself divides a(5).

Crossrefs

Sequence in context: A355439 A062928 A004899 * A004910 A120024 A062929

Adjacent sequences: A085078 A085079 A085080 * A085082 A085083 A085084

Keyword

nonn

Author

Amarnath Murthy, Jul 01 2003

Extensions

More terms from David Wasserman, Jan 18 2005

Status

approved