A114425 Product of the first n 3-almost primes (A014612).

8, 96, 1728, 34560, 933120, 26127360, 783820800, 32920473600, 1448500838400, 65182537728000, 3259126886400000, 169474598092800000, 10676899679846400000, 704675378869862400000, 47917925763150643200000

Offset: 1

Author

Jonathan Vos Post, Feb 13 2006

Keywords

• easy
• nonn

Comments

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.

Examples

			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).
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).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..364

Crossrefs

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

Programs

Mathematica

FoldList[Times,Select[Range[70],PrimeOmega[#]==3&]] (* Harvey P. Dale, Apr 26 2020 *)

Formula

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