A114421 Quintuple primorial n##### = n#5.

1, 2, 3, 5, 7, 11, 26, 51, 95, 161, 319, 806, 1887, 3895, 6923, 14993, 42718, 111333, 237595, 463841, 1064503, 3118414, 8795307, 19720385, 41281849, 103256791, 314959814, 905916621, 2110081195, 4499721541, 11668017383

Offset

0,2

Comments

This is to quintuple factorial A085157 = 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#5)*((n-1)#5)*((n-2)#5)*((n-3)#5)*((n-4)#5) = n#. n#5 is a k-almost prime for k = ceiling(n/5).

Links

Table of n, a(n) for n=0..30.

Eric Weisstein's World of Mathematics, Primorial.

Eric Weisstein's World of Mathematics, Multifactorial.

Formula

a(n) = n##### = prime(n)*((n-5)#####) = Prod[i == n mod 5, to n] prime(i). Notationally, prime(0) = 1; (-n)##### = 0#### = 1.

Example

n##### is also written n#5.
0#5 = p(0) = 1.
1#5 = p(1) = 2.
2#5 = p(2) = 3.
3#5 = p(3) = 5.
4#5 = p(4) = 7.
5#5 = p(5)p(0) = 11*1 = 11.
6#5 = p(6)p(1) = 13*2 = 26.
7#5 = p(7)p(2) = 17*3 = 51.
8#5 = p(8)p(3) = 19*5 = 95.
9#5 = p(9)p(4) = 23*7 = 161.
10#5 = p(10)p(5)p(0) = 29*11*1 = 319.
11#5 = p(11)p(6)p(1) = 31*13*2 = 806.
12#5 = 37*17*3 = 1887.
13#5 = 41*19*5 = 3895.
14#5 = 43*23*7 = 6923.
15#5 = 47*29*11*1 = 14993.
16#5 = 53*31*13*2 = 42718.
17#5 = 59*37*17*3 = 111333.
18#5 = 61*41*19*5 = 237595.
19#5 = 67*43*23*7 = 463841.
20#5 = 71*47*29*11*1 = 1064503.
21#5 = 73*53*31*13*2 = 3118414.
22#5 = 79*59*37*17*3 = 8795307.
23#5 = 83*61*41*19*5 = 19720385.
24#5 = 89*67*43*23*7 = 41281849.
25#5 = 97*71*47*29*11*1 = 103256791.
26#5 = 101*73*53*31*13*2 = 314959814.
27#5 = 103*79*59*37*17*3 = 905916621.
28#5 = 107*83*61*41*19*5 = 2110081195.
29#5 = 109*89*67*43*23*7 = 4499721541.
30#5 = 113*97*71*47*29*11*1 = 11668017383.

Crossrefs

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

Sequence in context: A373044 A378774 A036342 * A167119 A165682 A296924

Adjacent sequences: A114418 A114419 A114420 * A114422 A114423 A114424

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 12 2006

Status

approved