A060795 Write product of first n primes as x*y with x<y and x maximal; sequence gives value of 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

1,2

Comments

Or, lower central divisor of n-th primorial.

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

Links

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

Formula

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

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

Example

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A047046 A063545 A061058 * A071743 A071747 A071751

Adjacent sequences: A060792 A060793 A060794 * A060796 A060797 A060798

Keyword

nonn

Author

Labos Elemer, Apr 27 2001

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

Status

approved