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Superprimorials squared.
3

%I #7 Mar 23 2014 04:56:18

%S 1,4,144,129600,5715360000,30497732496000000,

%T 27502882612852046400000000,7167813920637790505994548640000000000,

%U 674376505248717910810215697948155164304000000000000,33564007734235791949707248640534383334045138980782017600000000000000

%N Superprimorials squared.

%C Square of product of first n primorials = A006939(n)^2.

%C Smallest number with n distinct even exponents in its prime factorization.

%C The prime version of Ramanujan's infinite nested radical 1*sqrt(1+2*sqrt(1+3*sqrt(1+…)))) is 2*sqrt(1+3*sqrt(1+5*sqrt(1+…))) = sqrt(4+sqrt(144+sqrt(129600+…))) = sqrt(a(1)+sqrt(a(2)+sqrt(a(3)+…))). See A239349 and A055209.

%H Vincenzo Librandi, <a href="/A239350/b239350.txt">Table of n, a(n) for n = 0..27</a>

%F a(n) = Product_{k=1..n} A002110(k)^2 = Product_{k=1..n} prime(k)^(2(n-k+1)).

%t Rest[FoldList[Times, 1, FoldList[Times, 1, Prime[Range[9]]^2]]]

%Y Cf. A002110, A055209, A006939, A239349.

%K nonn

%O 0,2

%A _Jonathan Sondow_, Mar 22 2014