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%I #5 Mar 30 2012 18:40:41
%S 2,12,216,8640,933120,209018880,100329062400,130026464870400,
%T 349511137571635200,1968446726803449446400,22676506292775737622528000,
%U 522466704985552994823045120000,27820307107070725868337506549760000
%N Partial products of A101695.
%C The number of prime factors (with multiplicity) of a(n) is T(n) = A000217(n) = n*(n+1)/2.
%F a(n) = Prod[i=1..n] i-th i-almost prime = Prod[i=1..n] A101695(i).
%e a(1) = 2 = prime(1).
%e a(2) = 12 = 2 * 6 = prime(1) * semiprime(2) = 2^2 * 3.
%e a(3) = 216 = 2 * 6 * 18 = prime(1) * semiprime(2) * 3-almostprime(3) = 2^3 * 3^3.
%e a(4) = 8640 = 2 * 6 * 18 * 40 = prime(1) * semiprime(2) * 3-almostprime(3) * 4-almostprime(4) = 2^6 * 3^3 * 5.
%e a(15) = 893179304874387947794472921245209518407680000 = 2 * 6 * 18 * 40 * 108 * 224 * 480 * 1296 * 2688 * 5632 * 11520 * 23040 * 53248 * 124416 * 258048 = 2^88 * 3^23 * 5^4 * 7^3 * 11 * 13.
%Y Cf. A000040, A001358, A014612, A014613, A046314, A046306, A046308, A046310, A046312, A046314, A069272, A069273, A069274, A069275, A069276, A069277, A069278, A069279, A069280, A069281, A101637, A101638, A101605, A101606, A101695.
%K nonn
%O 1,1
%A _Jonathan Vos Post_, Sep 28 2006
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