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A060795 Write product of first n primes as x*y with x<y and x maximal; sequence gives value of x. 14
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Or, lower central divisor of n-th primorial.
Subsequence of A005117 (squarefree numbers). - Michel Marcus, Feb 22 2016
LINKS
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
Sequence in context: A047046 A063545 A061058 * A071743 A071747 A071751
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

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Last modified April 21 12:42 EDT 2024. Contains 371870 sequences. (Running on oeis4.)