A114425 - OEIS

%I #10 Apr 26 2020 13:32:26

%S 8,96,1728,34560,933120,26127360,783820800,32920473600,1448500838400,

%T 65182537728000,3259126886400000,169474598092800000,

%U 10676899679846400000,704675378869862400000,47917925763150643200000

%N Product of the first n 3-almost primes (A014612).

%C 3-almost prime analog of primorial (A002110). The semiprime analog of primorial is A112141. Equivalent for product of what A086062 is for sum. Bigomega(a(n)) = the number of not necessarily distinct prime factors of a(n) = A001222(a(n)) = A008585(n) = 3*n.

%H Harvey P. Dale, <a href="/A114425/b114425.txt">Table of n, a(n) for n = 1..364</a>

%F a(n) = Prod[from i = 1 to n] A014612(i).

%e a(5) = 933120 = 8 * 12 * 18 * 20 * 27 = the product of the first 5 values of the 3-almost primes = 2^8 * 3^6 * 5, which has 3*5 = 15 prime factors (with multiplicity).

%e a(20) = 137199755075271237225676800000000 = 8 * 12 * 18 * 20 * 27 * 28 * 30 * 42 * 44 * 45 * 50 * 52 * 63 * 66 * 68 * 70 * 75 * 76 * 78 * 92 = 2^26 * 3^15 * 5^8 * 7^4 * 11, which has 20*3 = 60 prime factors (with multiplicity).

%t FoldList[Times,Select[Range[70],PrimeOmega[#]==3&]] (* _Harvey P. Dale_, Apr 26 2020 *)

%Y Cf. A002110, A008585, A014612, A086062, A112141.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Feb 13 2006