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a(n) is smallest number A such that there is an equality of the form (A=Product of n distinct primes) = (B=Product of n distinct primes) + (C=Product of n distinct primes) with gcd(A,B) = gcd(B,C) = gcd(A,C) = 1, B < C.
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%I #12 Oct 18 2019 00:15:31

%S 5,55,1105,32045,1626905,86522095,6738381681

%N a(n) is smallest number A such that there is an equality of the form (A=Product of n distinct primes) = (B=Product of n distinct primes) + (C=Product of n distinct primes) with gcd(A,B) = gcd(B,C) = gcd(A,C) = 1, B < C.

%e n..a(n)=A......B...........C...........A=B+C factorized

%e 1..5...........2...........3...........(5)=(2)+(3)

%e 2..55..........21..........34..........(5*11)=(3*7)+(2*17)

%e 3..1105........231.........874.........(5*13*17)=(3*7*11)+(2*19*23)

%e 4..32045.......15686.......16359.......(5*13*17*29)=(2*11*23*31)+(3*7*19*41)

%e 5..1626905.....397358......1229547.....(5*7*23*43*47)=(2*13*17*29*31)+(3*11*19*37*53)

%e 6..86522095....35750533....50771562....(5*11*17*37*41*61)=(7*13*19*23*29*31)+(2*3*43*47*53*79)

%e 7..6738381681..3218793466..3519588215..(3*17*29*31*47*53*59)=(2*7*23*37*43*61*103)+(5*11*13*19*41*71*89)

%Y Cf. A056602, A069717, A069718.

%K more,nonn

%O 1,1

%A _Naohiro Nomoto_, Aug 21 2000

%E a(5)-a(6) from _Lars Blomberg_, Oct 17 2015

%E a(7) from _Lars Blomberg_, Oct 20 2015