A114420 Quadruple primorial n#### = n#4.

1, 2, 3, 5, 7, 22, 39, 85, 133, 506, 1131, 2635, 4921, 20746, 48633, 123845, 260813, 1224014, 2966613, 8297615, 18517723, 89353022, 234362427, 688702045, 1648077347, 8667243134, 23670605127, 70936310635, 176344276129

Offset: 0

Author

Jonathan Vos Post, Feb 12 2006

Keywords

• easy
• nonn

Comments

This is to quadruple factorial A007662 = 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-3)####) = n#. n#### is a k-almost prime for k = ceiling(n/4).

Examples

			n#### is also written n#4.
0#### = p(0) = 1.
1#### = p(1) = 2.
2#### = p(2) = 3.
3#### = p(3) = 5.
4#### = p(4)p(0) = 7*1 = 7.
5#### = p(5)p(1) = 11*2 = 22.
6#### = p(6)p(2) = 13*3 = 39.
7#### = p(7)p(3) = 17*5 = 85.
8#### = p(8)p(4)p(0) = 19*7*1 = 133.
9#### = p(9)p(5)p(1) = 23*11*2 = 506.
10#### = p(10)p(6)p(2) = 29*13*3 = 1131.
11#### = p(11)p(7)p(3) = 31*17*5 = 2635.
12#### = 37*19*7*1 = 4921.
13#### = 41*23*11*2 = 20746.
14#### = 43*29*13*3 = 48633.
15#### = 47*31*17*5 = 123845.
16#### = 53*37*19*7*1 = 260813.
17#### = 59*41*23*11*2 = 1224014.
18#### = 61*43*29*13*3 = 2966613.
19#### = 67*47*31*17*5 = 8297615.
20#### = 71*53*37*19*7*1 = 18517723.
21#### = 73*59*41*23*11*2 = 89353022.
22#### = 79*61*43*29*13*3 = 234362427.
23#### = 83*67*47*31*17*5 = 688702045.
24#### = 89*71*53*37*19*7*1 = 1648077347.
25#### = 97*73*59*41*23*11*2 = 8667243134.
26#### = 101*79*61*43*29*13*3 = 23670605127.
27#### = 103*83*67*47*31*17*5 = 70936310635.
28#### = 107*89*71*53*37*19*7*1 = 176344276129.
		

Links

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

Crossrefs

Cf. A000142, A002110, A006882, A007661, A007662, A079078.

Formula

a(n) = n#### = prime(n)*((n-4)####) = Prod[i == n mod 4, to n] prime(i). Notationally, prime(0) = 1; (-n)#### = 0#### = 1.