A060795 Write product of first n primes as x*y with x

1, 2, 5, 14, 42, 165, 714, 3094, 14858, 79534, 447051, 2714690, 17395070, 114371070, 783152070, 5708587335, 43848093003, 342444658094, 2803119896185, 23619540863730, 201813981102615, 1793779293633437, 16342050964565645, 154170926013430326, 1518409177581024365

Offset: 1

Author

Labos Elemer, Apr 27 2001

Keywords

• nonn

Comments

Or, lower central divisor of n-th primorial.

Subsequence of A005117 (squarefree numbers). - Michel Marcus, Feb 22 2016

Examples

			n = 8: q(8) = 2*3*5*7*11*13*17*19 = 9699690. Its 128th and 129th divisors are {3094, 3135}: a(8) = 3094 and 3094 < A000196(9699690) = 3114 < 3135. [Corrected by _Colin Barker_, Oct 22 2010]
2*3*5*7 = 210 = 14*15 with difference of 1, so a(4) = 14.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..70

Crossrefs

Cf. A000196, A060776, A060777, A061057, A060796 (y), A061060 (y-x), A182987 (x+y), A061030, A061031, A061032, A061033, A060755, A033677, A200743.

Programs

Maple

F:= proc(n) local P,N,M;
     P:= {seq(ithprime(i),i=1..n)};
     N:= floor(sqrt(convert(P,`*`)));
     M:= map(convert, combinat:-powerset(P),`*`);
     max(select(`<=`,M,N))
end proc:
map(F, [$1..20]); # Robert Israel, Feb 22 2016

Mathematica

a[n_] := (m = Times @@ Prime[Range[n]] ; dd = Divisors[m]; dd[[Length[dd]/2 // Floor]]); Table[Print[an = a[n]]; an, {n, 1, 25}] (* Jean-François Alcover, Oct 15 2016 *)

PARI

a(n) = my(m=prod(i=1, n, prime(i))); divisors(m)[numdiv(m)\2]; \\ Michel Marcus, Feb 22 2016

Formula

a(n) = A060775(A002110(n)). - Labos Elemer, Apr 27 2001

a(n) = A002110(n)/A060796(n). - M. F. Hasler, Mar 21 2022

Extensions

More terms from Ed Pegg Jr, May 28 2001

a(16)-a(23) computed by Jud McCranie, Apr 15 2000

a(24) and a(25) from Robert Israel, Feb 22 2016

a(25) corrected by Jean-François Alcover, Oct 15 2016

a(26)-a(33) in b-file from Amiram Eldar, Apr 09 2020

Up to a(38) using b-file of A060796, by M. F. Hasler, Mar 21 2022

a(39)-a(70) in b-file from Max Alekseyev, Apr 20 2022