A342876 Numbers that can be written as a product of k consecutive composite numbers and also of k+1 consecutive composite numbers, for some k>1.

1680, 4320, 120960, 166320, 175560, 215760, 725760, 1814400, 1080647568000, 104613949440000, 115880067072000

Offset: 1

Author

David A. Corneth, Mar 28 2021

Keywords

• nonn
• more

Comments

Similar to but different from A175340 which has an additional condition that says that factors cannot be used twice. So 1814400 is here via 8*9*10*12*14*15 = 15*16*18*20*21 but not there as 15 is used twice.

This sequence is infinite. Proof:

Choose two consecutive composites c1 and c2 such that c1 < c2. Let S be the composites strictly between c2 and c1 * c2. Let product(S) be the product of terms in S. Then c1 * c2 * product(S) is a term.

Crossrefs

Cf. A175340.