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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.
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%I #4 Dec 05 2013 19:56:18

%S 1,2,3,4,1680,2162160,586051200,5967561600,1220096908800,

%T 33371339479827148800,10221346459144248675287040000,

%U 1065516759202418135010355181075171069914644480000000

%N 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.

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

%C 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

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

%e a(4) itself divides a(5).

%K nonn

%O 1,2

%A _Amarnath Murthy_, Jul 01 2003

%E More terms from _David Wasserman_, Jan 18 2005