A114411 Triple primorial n### = n#3.

1, 2, 3, 5, 14, 33, 65, 238, 627, 1495, 6902, 19437, 55315, 282982, 835791, 2599805, 14998046, 49311669, 158588105, 1004869082, 3501128499, 11576931665, 79384657478, 290593665417, 1030346918185, 7700311775366, 29349960207117

Offset: 0

Author

Jonathan Vos Post, Feb 12 2006

Keywords

• nonn

Comments

This is to triple factorial A007661 = n!!!, as double primorial A079078 = n## is to double factorial A006882 = n!! and as primorial A002110 = n# is to factorial A000142 = n!. There is an obvious generalization to multiprimorial. (n###)*((n-1)###)*((n-2)###) = n#. n### is a k-almost prime for k = ceiling(n/3).

Examples

			n### is also written n#3.
0### = p(0) = 1.
1### = p(1) = 2.
2### = p(2) = 3.
3### = p(3)p(0) = 5*1 = 5.
4### = p(4)p(1) = 7*2 = 14.
5### = p(5)p(2) = 11*3 = 33.
6### = p(6)p(3)p(0) = 13*5*1 = 65.
7### = p(7)p(4)p(1) = 17*7*2 = 238.
8### = p(8)p(5)p(2) = 19*11*3 = 627.
9### = p(9)p(6)p(3)p(0) = 23*13*5*1 = 1495.
10### = p(10)p(7)p(4)p(1) = 29*17*7*2 = 6902.
11### = p(11)p(8)p(5)p(2) = 31*19*11*3 = 19437.
12### = 37*23*13*5*1 = 55315.
13### = 41*29*17*7*2 = 282982.
14### = 43*31*19*11*3 = 835791.
15### = 47*37*23*13*5*1 = 2599805.
27### = 106125732573055 = 5 * 13 * 23 * 37 * 47 * 61 * 73 * 89 * 103.
		

Links

• Eric Weisstein's World of Mathematics, Primorial.
• Eric Weisstein's World of Mathematics, Multifactorial.

Crossrefs

Cf. A000142, A002110, A006882, A007661, A079078.

Programs

Mathematica

a[0] = 1; a[1] = 2; a[2] = 3;
a[n_] := a[n - 3] * Prime[n]
Array[a, 27, 0] (* Jon Maiga, Aug 04 2019 *)

Formula

a(n) = n### = prime(n)*((n-3)###) = Prod[i == n mod 3, to n] prime(i). Notationally, prime(0) = 1; (-n)### = 0### = 1.