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Product of the first n 4-almost primes (A014613).
4

%I #8 Dec 02 2018 16:52:30

%S 16,384,13824,552960,29859840,1672151040,100329062400,8126654054400,

%T 682638940569600,60072226770124800,5406500409311232000,

%U 540650040931123200000,56227604256836812800000

%N Product of the first n 4-almost primes (A014613).

%C 4-almost prime analog of primorial (A002110). The semiprime analog of primorial is A112141. Equivalent for product of what A086046 is for sum. Bigomega(a(n)) = the number of not necessarily distinct prime factors of a(n) = A001222(a(n)) = A008586(n) = 4*n.

%F a(n) = Prod[from i = 1 to n] A014613(i).

%e a(5) = 29859840 = 16 * 24 * 36 * 40 * 54 = the product of the first 5 values of the 4-almost primes = 2^13 * 3^6 * 5, which has 4*5 = 20 prime factors (with multiplicity).

%t FoldList[Times,Select[Range[200],PrimeOmega[#]==4&]] (* _Harvey P. Dale_, Dec 02 2018 *)

%Y Cf. A001222, A002110, A008585, A014613, A008586, A086046, A112141.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Feb 13 2006