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

%I A060795 #59 Jan 14 2024 12:34:26
%S A060795 1,2,5,14,42,165,714,3094,14858,79534,447051,2714690,17395070,
%T A060795 114371070,783152070,5708587335,43848093003,342444658094,
%U A060795 2803119896185,23619540863730,201813981102615,1793779293633437,16342050964565645,154170926013430326,1518409177581024365
%N A060795 Write product of first n primes as x*y with x<y and x maximal; sequence gives value of x.
%C A060795 Or, lower central divisor of n-th primorial.
%C A060795 Subsequence of A005117 (squarefree numbers). - _Michel Marcus_, Feb 22 2016
%H A060795 Max Alekseyev, <a href="/A060795/b060795.txt">Table of n, a(n) for n = 1..70</a>
%F A060795 a(n) = A060775(A002110(n)). - _Labos Elemer_, Apr 27 2001
%F A060795 a(n) = A002110(n)/A060796(n). - _M. F. Hasler_, Mar 21 2022
%e A060795 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 A060795 2*3*5*7 = 210 = 14*15 with difference of 1, so a(4) = 14.
%p A060795 F:= proc(n) local P,N,M;
%p A060795      P:= {seq(ithprime(i),i=1..n)};
%p A060795      N:= floor(sqrt(convert(P,`*`)));
%p A060795      M:= map(convert, combinat:-powerset(P),`*`);
%p A060795      max(select(`<=`,M,N))
%p A060795 end proc:
%p A060795 map(F, [$1..20]); # _Robert Israel_, Feb 22 2016
%t A060795 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 A060795 (PARI) a(n) = my(m=prod(i=1, n, prime(i))); divisors(m)[numdiv(m)\2]; \\ _Michel Marcus_, Feb 22 2016
%Y A060795 Cf. A000196, A060776, A060777, A061057, A060796 (y), A061060 (y-x), A182987 (x+y), A061030, A061031, A061032, A061033, A060755, A033677, A200743.
%K A060795 nonn
%O A060795 1,2
%A A060795 _Labos Elemer_, Apr 27 2001
%E A060795 More terms from _Ed Pegg Jr_, May 28 2001
%E A060795 a(16)-a(23) computed by _Jud McCranie_, Apr 15 2000
%E A060795 a(24) and a(25) from _Robert Israel_, Feb 22 2016
%E A060795 a(25) corrected by _Jean-François Alcover_, Oct 15 2016
%E A060795 a(26)-a(33) in b-file from _Amiram Eldar_, Apr 09 2020
%E A060795 Up to a(38) using b-file of A060796, by _M. F. Hasler_, Mar 21 2022
%E A060795 a(39)-a(70) in b-file from _Max Alekseyev_, Apr 20 2022