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%I #8 Mar 28 2021 18:39:31
%S 1680,4320,120960,166320,175560,215760,725760,1814400,1080647568000,
%T 104613949440000,115880067072000
%N 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.
%C 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.
%C This sequence is infinite. Proof:
%C 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.
%Y Cf. A175340.
%K nonn,more
%O 1,1
%A _David A. Corneth_, Mar 28 2021