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A327486 Product of Omegas of positive integers from 2 to n. 6

%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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Last modified March 29 08:47 EDT 2024. Contains 371267 sequences. (Running on oeis4.)