%I #10 Sep 29 2019 12:20:14
%S 1,1,1,2,2,4,4,12,24,48,48,144,144,288,576,2304,2304,6912,6912,20736,
%T 41472,82944,82944,331776,663552,1327104,3981312,11943936,11943936,
%U 35831808,35831808,179159040,358318080,716636160,1433272320,5733089280,5733089280,11466178560
%N Product of Omegas of positive integers from 2 to n.
%C Omega(n) (A001222) is the number of prime factors of n, counted with multiplicity.
%C Also the number of ways to choose a prime factor, counting multiplicity, of each positive integer from 2 to n.
%F a(n > 1) = a(n - 1) * A001222(n).
%e We have a(8) = 1 * 1 * 2 * 1 * 2 * 1 * 3 = 12.
%p a:= proc(n) option remember; `if`(n<2, n,
%p numtheory[bigomega](n)*a(n-1))
%p end:
%p seq(a(n), n=1..40); # _Alois P. Heinz_, Sep 29 2019
%t Table[Product[PrimeOmega[k],{k,2,n}],{n,30}]
%o (PARI) a(n) = prod(k=2, n, bigomega(k)); \\ _Michel Marcus_, Sep 29 2019
%Y Partial products of A001222.
%Y Cf. A001221, A056239, A071625, A112798, A118914, A316413, A327485.
%K nonn
%O 1,4
%A _Gus Wiseman_, Sep 28 2019
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