%I #6 Mar 30 2012 18:40:35

%S 1,2,3,5,7,11,26,51,95,161,319,806,1887,3895,6923,14993,42718,111333,

%T 237595,463841,1064503,3118414,8795307,19720385,41281849,103256791,

%U 314959814,905916621,2110081195,4499721541,11668017383

%N Quintuple primorial n##### = n#5.

%C 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).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Primorial.html">Primorial.</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Multifactorial.html">Multifactorial.</a>

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

%e n##### is also written n#5.

%e 0#5 = p(0) = 1.

%e 1#5 = p(1) = 2.

%e 2#5 = p(2) = 3.

%e 3#5 = p(3) = 5.

%e 4#5 = p(4) = 7.

%e 5#5 = p(5)p(0) = 11*1 = 11.

%e 6#5 = p(6)p(1) = 13*2 = 26.

%e 7#5 = p(7)p(2) = 17*3 = 51.

%e 8#5 = p(8)p(3) = 19*5 = 95.

%e 9#5 = p(9)p(4) = 23*7 = 161.

%e 10#5 = p(10)p(5)p(0) = 29*11*1 = 319.

%e 11#5 = p(11)p(6)p(1) = 31*13*2 = 806.

%e 12#5 = 37*17*3 = 1887.

%e 13#5 = 41*19*5 = 3895.

%e 14#5 = 43*23*7 = 6923.

%e 15#5 = 47*29*11*1 = 14993.

%e 16#5 = 53*31*13*2 = 42718.

%e 17#5 = 59*37*17*3 = 111333.

%e 18#5 = 61*41*19*5 = 237595.

%e 19#5 = 67*43*23*7 = 463841.

%e 20#5 = 71*47*29*11*1 = 1064503.

%e 21#5 = 73*53*31*13*2 = 3118414.

%e 22#5 = 79*59*37*17*3 = 8795307.

%e 23#5 = 83*61*41*19*5 = 19720385.

%e 24#5 = 89*67*43*23*7 = 41281849.

%e 25#5 = 97*71*47*29*11*1 = 103256791.

%e 26#5 = 101*73*53*31*13*2 = 314959814.

%e 27#5 = 103*79*59*37*17*3 = 905916621.

%e 28#5 = 107*83*61*41*19*5 = 2110081195.

%e 29#5 = 109*89*67*43*23*7 = 4499721541.

%e 30#5 = 113*97*71*47*29*11*1 = 11668017383.

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

%K easy,nonn

%O 0,2

%A _Jonathan Vos Post_, Feb 12 2006