A060796 - OEIS

%I #74 Apr 20 2022 18:43:48

%S 2,3,6,15,55,182,715,3135,15015,81345,448630,2733549,17490603,

%T 114388729,785147363,5708795638,43850489690,342503171205,

%U 2803419704514,23622001517543,201817933409378,1793779635410490,16342166369958702,154171363634898185,1518410187442699518,15259831781575946565

%N Upper central divisor of n-th primorial.

%C Also: Write product of first n primes as x*y with x < y and x maximal; sequence gives value of y. Indeed, p(n)# = primorial(n) = A002110(n) is never a square for n >= 1; all exponents in the prime factorization are 1. Therefore 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+1-k)} 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^(n-1)+1)-th divisor, which is the smallest one larger than sqrt(p(n)#). - _M. F. Hasler_, Sep 20 2011

%H Max Alekseyev, <a href="/A060796/b060796.txt">Table of n, a(n) for n = 1..70</a>

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

%F a(n) = A002110(n)/A060795(n). - _M. F. Hasler_, Mar 21 2022

%e 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]

%t 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 *)

%o (PARI) A060796(n) = divisors(prod(k=1,n,prime(k)))[2^(n-1)+1] \\ Requires stack size > 2^(n+5). - _M. F. Hasler_, Sep 20 2011

%Y Cf. A060755, A000196, A002110, A033677, A060776, A060777, A061057, A060795 (x), A061060 (y-x), A182987 (x+y), A061030, A061031, A061032, A061033, A200744.

%K nonn

%O 1,1

%A _Labos Elemer_, Apr 27 2001

%E More terms from _Ryan Propper_, Jul 25 2005

%E a(24)-a(37) in b-file calculated from A182987 by _M. F. Hasler_, Sep 20 2011

%E a(38) from _David A. Corneth_, Mar 21 2022

%E a(39)-a(70) in b-file from _Max Alekseyev_, Apr 20 2022