0,2

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).

Eric Weisstein's World of Mathematics, Primorial.

Eric Weisstein's World of Mathematics, Multifactorial.

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

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.

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

Adjacent sequences: A114408 A114409 A114410 this_sequence A114412 A114413 A114414

Sequence in context: A126333 A039575 A104870 this_sequence A099410 A102033 A072246

nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Feb 12 2006