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%I #7 Mar 31 2012 13:50:36
%S 10,231,2958,226083
%N Numbers A such that there is an equation of the form (A = Product of m + 1 primes) = (B = Product of m primes) + (C = Product of m primes), where A*B*C is a primorial number (A002110).
%C Terms have been verified. There are no additional terms for m <= 7. - _Rick L. Shepherd_, Jun 16 2008
%C (C(3m+1,m+1)*C(2m,m))/(C(3m-2,m)*C(2m-2,m-1)) = (27m^2-1)/(m^2+1), so for a brute-force search for large m, about 27 times as many cases must be examined for m as for m-1. - _Rick L. Shepherd_, Jun 16 2008
%e 10 = (2*5) = 3+7;
%e 231 = (3*7*11) = (2*5)+(13*17);
%e 2958 = (2*3*17*29) = (5*13*23)+(7*11*19);
%e 226083 = (3*11*13*17*31) = (2*7*19*23)+(5*29*37*41).
%Y Cf. A057035, A056600, A002110.
%K more,nonn
%O 1,1
%A _Naohiro Nomoto_, Aug 21 2000
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