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 A182987 Least a+b such that ab=A002110(n), the product of the first n primes; a,b being positive integers. 5
 2, 3, 5, 11, 29, 97, 347, 1429, 6229, 29873, 160879, 895681, 5448239, 34885673, 228759799, 1568299433, 11417382973, 87698582693, 684947829299, 5606539600699, 47241542381273, 403631914511993, 3587558929043927, 32684217334524347, 308342289648328511, 3036819365023723883 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Original definition (not applicable for n=0 and n=1, but equivalent for n>=2): Let p(S) be product of integers in S. a(n) is minimum of p(S_1) + p(S_2) over all partitions of first n primes into sets S_1 and S_2. Also: Least integer such that a(n)^2-4*A002110(n) is a square. [David Broadhurst, Sep 20 2011] The integers a,b are the two median divisors of primorial(n), a=A060795(n)=A060775(A002110(n)) and b=A060796(n)=A033677(A002110(n)). (For n=0, a=b=1 of course.) - M. F. Hasler, Sep 20 2011 LINKS D. Broadhurst, Re: adding to prime number [primes in A182987], primenumbers group, Sep 20 2011. FORMULA a(n) = A060795(n) + A060796(n). - M. F. Hasler, Sep 20 2011 EXAMPLE a(3) = 11 = min{ 2*3 + 5 = 11, 2*5 + 3 = 13, 3*5 + 2 = 17 } Or, a(3) = 11 = min { 1+30, 2+15, 3+10, 5+6 } because A002110(3) = 2*3*5 = 30 = 2*15 = 3*10 = 5*6. MATHEMATICA a[0] = 2; a[n_] := Module[{m = Times @@ Prime[Range[n]]}, For[an = 2 Floor[Sqrt[m]] + 1, an <= m + 2, an += 2, If[IntegerQ[Sqrt[an^2 - 4 m]], Return[an]]]]; Table[an = a[n]; Print[an]; an, {n, 0, 25}] (* Jean-François Alcover, Oct 20 2016, adapted from PARI *) PROG (PARI) A182987(n)={n=divisors(prod(i=1, n, prime(i))); n[max(#n\2, 1)]+n[#n\2+1]}  \\ M. F. Hasler, Sep 20 2011 (PARI) A182987(n)={ n||return(2); my(m=prod(k=1, n, prime(k))); forstep(a=2*sqrtint(m)+1, m+2, 2, issquare(a^2-4*m) & return(a)) }  \\ M. F. Hasler, following an idea from David Broadhurst, Sep 20 2011 CROSSREFS Cf. A173631. Sequence in context: A265418 A190197 A173631 * A087580 A072535 A073680 Adjacent sequences:  A182984 A182985 A182986 * A182988 A182989 A182990 KEYWORD nonn AUTHOR Risto Kauppila, Feb 06 2011 EXTENSIONS First term and example corrected, as empty sets have product 1, by Phil Carmody, Sep 20 2011 Simpler definition and extension to n=0 by M. F. Hasler, Sep 20 2011 STATUS approved

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Last modified October 18 07:42 EDT 2019. Contains 328146 sequences. (Running on oeis4.)