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Revision History for A239350

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A239350

Superprimorials squared.
(history; published version)

#7 by Joerg Arndt at Sun Mar 23 04:56:18 EDT 2014

STATUS

proposed

approved

#6 by Vincenzo Librandi at Sun Mar 23 04:27:48 EDT 2014

STATUS

editing

proposed

#5 by Vincenzo Librandi at Sun Mar 23 04:27:37 EDT 2014

LINKS

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

STATUS

approved

editing

#4 by Michael Somos at Sun Mar 23 01:47:34 EDT 2014

STATUS

proposed

approved

#3 by Jonathan Sondow at Sat Mar 22 19:37:18 EDT 2014

STATUS

editing

proposed

#2 by Jonathan Sondow at Sat Mar 22 19:37:14 EDT 2014

NAME

allocated for Jonathan Sondow

Superprimorials squared.

DATA

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

OFFSET

0,2

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.

FORMULA

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

MATHEMATICA

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

CROSSREFS

Cf. A002110, A055209, A006939, A239349.

KEYWORD

allocated

nonn

AUTHOR

Jonathan Sondow, Mar 22 2014

STATUS

approved

editing

#1 by Jonathan Sondow at Sun Mar 16 18:39:44 EDT 2014

NAME

allocated for Jonathan Sondow

KEYWORD

allocated

STATUS

approved