A085895 - OEIS

A085895

Group the natural numbers such that the product of the n-th group is divisible by 2^n. (1), (2), (3,4), (5,6,7,8), (9,10,11,12,13,14),(15,16,17,18), ... Sequence contains the product of the terms of the groups.

1, 2, 12, 1680, 2162160, 73440, 96909120, 424097856000, 5339572260422400, 57407703889536000, 1573144097507348889600, 89247024757574635311360000, 131197375012291112448000, 6932022668773077815267328000

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..13.

FORMULA

From Chayim Lowen, Jul 29 2015: (Start)

Product_{m=0..n} a(m) = (A085897(n+1)-1)! whence:

a(n) = (A085897(n+1)-1)!/a(n-1).

a(n) = (A085897(n+1)-1)!/(A085897(n)-1)!. (End)

EXAMPLE

a(3) = 1680 = 5*6*7*8 = 2^3*(5*6*7) is divisible by 2^3=8. (In fact, it is divisible by 2^4, but 5*6*7 is not divisible by 8.)