A239350 Superprimorials squared.

1, 4, 144, 129600, 5715360000, 30497732496000000, 27502882612852046400000000, 7167813920637790505994548640000000000, 674376505248717910810215697948155164304000000000000, 33564007734235791949707248640534383334045138980782017600000000000000

Offset: 0

Author

Jonathan Sondow, Mar 22 2014

Keywords

• nonn

Comments

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

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

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.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..27

Crossrefs

Cf. A002110, A055209, A006939, A239349.

Programs

Mathematica

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

Formula

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