A060795 - OEIS

%I #59 Jan 14 2024 12:34:26

%S 1,2,5,14,42,165,714,3094,14858,79534,447051,2714690,17395070,

%T 114371070,783152070,5708587335,43848093003,342444658094,

%U 2803119896185,23619540863730,201813981102615,1793779293633437,16342050964565645,154170926013430326,1518409177581024365

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

%C Or, lower central divisor of n-th primorial.

%C Subsequence of A005117 (squarefree numbers). - _Michel Marcus_, Feb 22 2016

%H Max Alekseyev, <a href="/A060795/b060795.txt">Table of n, a(n) for n = 1..70</a>

%F a(n) = A060775(A002110(n)). - _Labos Elemer_, Apr 27 2001

%F a(n) = A002110(n)/A060796(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) = 3094 and 3094 < A000196(9699690) = 3114 < 3135. [Corrected by _Colin Barker_, Oct 22 2010]

%e 2*3*5*7 = 210 = 14*15 with difference of 1, so a(4) = 14.

%p F:= proc(n) local P,N,M;

%p      P:= {seq(ithprime(i),i=1..n)};

%p      N:= floor(sqrt(convert(P,`*`)));

%p      M:= map(convert, combinat:-powerset(P),`*`);

%p      max(select(`<=`,M,N))

%p end proc:

%p map(F, [$1..20]); # _Robert Israel_, Feb 22 2016

%t 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 *)

%o (PARI) a(n) = my(m=prod(i=1, n, prime(i))); divisors(m)[numdiv(m)\2]; \\ _Michel Marcus_, Feb 22 2016

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

%K nonn

%O 1,2

%A _Labos Elemer_, Apr 27 2001

%E More terms from _Ed Pegg Jr_, May 28 2001

%E a(16)-a(23) computed by _Jud McCranie_, Apr 15 2000

%E a(24) and a(25) from _Robert Israel_, Feb 22 2016

%E a(25) corrected by _Jean-François Alcover_, Oct 15 2016

%E a(26)-a(33) in b-file from _Amiram Eldar_, Apr 09 2020

%E Up to a(38) using b-file of A060796, by _M. F. Hasler_, Mar 21 2022

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