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A060795
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Write product of first n primes as x*y with x<y and x maximal; sequence gives value of x.
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14
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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
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OFFSET
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1,2
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COMMENTS
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Or, lower central divisor of n-th primorial.
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LINKS
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FORMULA
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EXAMPLE
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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.
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MAPLE
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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:
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n) = my(m=prod(i=1, n, prime(i))); divisors(m)[numdiv(m)\2]; \\ Michel Marcus, Feb 22 2016
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CROSSREFS
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Cf. A000196, A060776, A060777, A061057, A060796 (y), A061060 (y-x), A182987 (x+y), A061030, A061031, A061032, A061033, A060755, A033677, A200743.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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