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%I #6 Mar 30 2012 18:40:35
%S 1,2,3,5,7,22,39,85,133,506,1131,2635,4921,20746,48633,123845,260813,
%T 1224014,2966613,8297615,18517723,89353022,234362427,688702045,
%U 1648077347,8667243134,23670605127,70936310635,176344276129
%N Quadruple primorial n#### = n#4.
%C 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).
%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-4)####) = Prod[i == n mod 4, to n] prime(i). Notationally, prime(0) = 1; (-n)#### = 0#### = 1.
%e n#### is also written n#4.
%e 0#### = p(0) = 1.
%e 1#### = p(1) = 2.
%e 2#### = p(2) = 3.
%e 3#### = p(3) = 5.
%e 4#### = p(4)p(0) = 7*1 = 7.
%e 5#### = p(5)p(1) = 11*2 = 22.
%e 6#### = p(6)p(2) = 13*3 = 39.
%e 7#### = p(7)p(3) = 17*5 = 85.
%e 8#### = p(8)p(4)p(0) = 19*7*1 = 133.
%e 9#### = p(9)p(5)p(1) = 23*11*2 = 506.
%e 10#### = p(10)p(6)p(2) = 29*13*3 = 1131.
%e 11#### = p(11)p(7)p(3) = 31*17*5 = 2635.
%e 12#### = 37*19*7*1 = 4921.
%e 13#### = 41*23*11*2 = 20746.
%e 14#### = 43*29*13*3 = 48633.
%e 15#### = 47*31*17*5 = 123845.
%e 16#### = 53*37*19*7*1 = 260813.
%e 17#### = 59*41*23*11*2 = 1224014.
%e 18#### = 61*43*29*13*3 = 2966613.
%e 19#### = 67*47*31*17*5 = 8297615.
%e 20#### = 71*53*37*19*7*1 = 18517723.
%e 21#### = 73*59*41*23*11*2 = 89353022.
%e 22#### = 79*61*43*29*13*3 = 234362427.
%e 23#### = 83*67*47*31*17*5 = 688702045.
%e 24#### = 89*71*53*37*19*7*1 = 1648077347.
%e 25#### = 97*73*59*41*23*11*2 = 8667243134.
%e 26#### = 101*79*61*43*29*13*3 = 23670605127.
%e 27#### = 103*83*67*47*31*17*5 = 70936310635.
%e 28#### = 107*89*71*53*37*19*7*1 = 176344276129.
%Y Cf. A000142, A002110, A006882, A007661, A007662, A079078.
%K easy,nonn
%O 0,2
%A _Jonathan Vos Post_, Feb 12 2006