

A060796


Upper central divisor of nth primorial.


4



2, 3, 6, 15, 55, 182, 715, 3135, 15015, 81345, 448630, 2733549, 17490603, 114388729, 785147363, 5708795638, 43850489690, 342503171205, 2803419704514, 23622001517543, 201817933409378, 1793779635410490, 16342166369958702
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OFFSET

1,1


COMMENTS

Also: Write product of first n primes as x*y with x<y and x maximal; sequence gives value of y. This was sequence A061059, which is a duplicate of this sequence. Indeed, p(n)# = primorial(n) = A002110(n) is never a square, it has N=2^n distinct divisors. Since this is an even number, the N divisors can be grouped in N/2 pairs {d(k), d(N+1k)} with product equal to p(n)#. Obviously, one of the two is always smaller and one is larger than sqrt(p(n)#). This sequence gives the (2^(n1)+1)th divisor, which is the smallest one larger than sqrt(p(n)#).  M. F. Hasler, Sep 20 2011
Further terms (calculated from A182987):
a(24) = 154171363634898185,
a(25) = 1518410187442699518,
a(26) = 15259831781575946565,
a(27) = 154870358790203939190,
a(28) = 1601991507050573600715,
a(29) = 16725281357261594271714,
a(30) = 177792170427340904920562,
a(31) = 2003615968659851168928690,
a(32) = 22932432917001897051097491,
a(33) = 268417245982598363846820345,
a(34) = 3164592660873444717893657954,
a(35) = 38628776202993992477961504201,
a(37) = 5947702665851804982553152089030.  M. F. Hasler, Sep 20 2011


LINKS

Table of n, a(n) for n=1..23.


FORMULA

a(n) = A033677(A002110(n)).


EXAMPLE

n=8, q(8)=2.3.5.7.11.13.17.19=9699690. Its 128th and 129th divisors are {3094,3135}: a(8)=3135, and 3094 < A000196(9699690) = 3114 < 3135. [Corrected by M. F. Hasler, Sep 20 2011]


MATHEMATICA

k = 1; Do[k *= Prime[n]; l = Divisors[k]; x = Length[l]; Print[l[[x/2 + 1]]], {n, 1, 24}] (*R. Propper, 2005*)


PROG

(PARI) A060796(n) = divisors(prod(k=1, n, prime(k)))[2^(n1)+1] \\ M. F. Hasler, Sep 20 2011


CROSSREFS

Cf. A060755, A000196, A033677.
Cf. A061055, A061056, A061057, A061058, A061059, A061060, A061030, A061031, A061032, A061033.
Sequence in context: A121688 A082094 * A061059 A059842 A001529 A069354
Adjacent sequences: A060793 A060794 A060795 * A060797 A060798 A060799


KEYWORD

nonn,changed


AUTHOR

Labos Elemer, Apr 27 2001


EXTENSIONS

More terms from Ryan Propper, Jul 25 2005


STATUS

approved



