This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A114421 #7 Feb 16 2025 08:32:59 %S A114421 1,2,3,5,7,11,26,51,95,161,319,806,1887,3895,6923,14993,42718,111333, %T A114421 237595,463841,1064503,3118414,8795307,19720385,41281849,103256791, %U A114421 314959814,905916621,2110081195,4499721541,11668017383 %N A114421 Quintuple primorial n##### = n#5. %C A114421 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 A114421 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Primorial.html">Primorial.</a> %H A114421 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Multifactorial.html">Multifactorial.</a> %F A114421 a(n) = n##### = prime(n)*((n-5)#####) = Prod[i == n mod 5, to n] prime(i). Notationally, prime(0) = 1; (-n)##### = 0#### = 1. %e A114421 n##### is also written n#5. %e A114421 0#5 = p(0) = 1. %e A114421 1#5 = p(1) = 2. %e A114421 2#5 = p(2) = 3. %e A114421 3#5 = p(3) = 5. %e A114421 4#5 = p(4) = 7. %e A114421 5#5 = p(5)p(0) = 11*1 = 11. %e A114421 6#5 = p(6)p(1) = 13*2 = 26. %e A114421 7#5 = p(7)p(2) = 17*3 = 51. %e A114421 8#5 = p(8)p(3) = 19*5 = 95. %e A114421 9#5 = p(9)p(4) = 23*7 = 161. %e A114421 10#5 = p(10)p(5)p(0) = 29*11*1 = 319. %e A114421 11#5 = p(11)p(6)p(1) = 31*13*2 = 806. %e A114421 12#5 = 37*17*3 = 1887. %e A114421 13#5 = 41*19*5 = 3895. %e A114421 14#5 = 43*23*7 = 6923. %e A114421 15#5 = 47*29*11*1 = 14993. %e A114421 16#5 = 53*31*13*2 = 42718. %e A114421 17#5 = 59*37*17*3 = 111333. %e A114421 18#5 = 61*41*19*5 = 237595. %e A114421 19#5 = 67*43*23*7 = 463841. %e A114421 20#5 = 71*47*29*11*1 = 1064503. %e A114421 21#5 = 73*53*31*13*2 = 3118414. %e A114421 22#5 = 79*59*37*17*3 = 8795307. %e A114421 23#5 = 83*61*41*19*5 = 19720385. %e A114421 24#5 = 89*67*43*23*7 = 41281849. %e A114421 25#5 = 97*71*47*29*11*1 = 103256791. %e A114421 26#5 = 101*73*53*31*13*2 = 314959814. %e A114421 27#5 = 103*79*59*37*17*3 = 905916621. %e A114421 28#5 = 107*83*61*41*19*5 = 2110081195. %e A114421 29#5 = 109*89*67*43*23*7 = 4499721541. %e A114421 30#5 = 113*97*71*47*29*11*1 = 11668017383. %Y A114421 Cf. A000142, A002110, A006882, A007661, A007662, A079078. %K A114421 easy,nonn %O A114421 0,2 %A A114421 _Jonathan Vos Post_, Feb 12 2006