

A060796


Upper central divisor of nth primorial.


6



2, 3, 6, 15, 55, 182, 715, 3135, 15015, 81345, 448630, 2733549, 17490603, 114388729, 785147363, 5708795638, 43850489690, 342503171205, 2803419704514, 23622001517543, 201817933409378, 1793779635410490, 16342166369958702, 154171363634898185, 1518410187442699518, 15259831781575946565
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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 originally a separate sequence, A061059. Indeed, p(n)# = primorial(n) = A002110(n) is never a square for n >= 1; all exponents in the prime factorization are 1. The latter gives primorial(n) 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)#. 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


LINKS

David A. Corneth, Table of n, a(n) for n = 1..38 (first 37 terms from M. F. Hasler)


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}] (* Ryan Propper, Jul 25 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, A060796, A061060, A061030, A061031, A061032, A061033.
Sequence in context: A082094 A320963 A061059 * A059842 A001529 A069354
Adjacent sequences: A060793 A060794 A060795 * A060797 A060798 A060799


KEYWORD

nonn


AUTHOR

Labos Elemer, Apr 27 2001


EXTENSIONS

More terms from Ryan Propper, Jul 25 2005
Further terms a(24) .. a(37) calculated from A182987: cf. bfile.  M. F. Hasler, Sep 20 2011


STATUS

approved



