0,2

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).

Eric Weisstein's World of Mathematics, Primorial.

Eric Weisstein's World of Mathematics, Multifactorial.

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

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.

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

Sequence in context: A079148 A107367 A036342 this_sequence A099160 A028911 A028912

Adjacent sequences: A114418 A114419 A114420 this_sequence A114422 A114423 A114424

easy,nonn

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