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%I #26 Mar 01 2014 05:27:44
%S 31,71,151,191,311,1031,1991,3191,5351,5591,10391,15791,17111,27191,
%T 31391,35591,42311,50951,70391,93551,107159,117911,119831,126551,
%U 166871,180311,191831,216191,255191,259871,327071,366791,435431,465911,514751,576551,599231,631991
%N Numbers which can be decomposed as pq + qr + rp (where p < q < r are distinct primes) in more ways than any smaller number.
%C Records in A238403.
%e 71 = 3*5 + 3*7 + 5*7 = 2*3 + 2*13 + 3*13 can be written in two ways, while smaller numbers can be written in at most one way.
%o (PARI) do(n)=my(v=vectorsmall(n),r); forprime(r=5,(n-6)\5, forprime(q=3, min((n-2*r)\(r+2),r-2), my(S=q+r,P=q*r); forprime(p=2,min((n-P)\S,q-1), v[p*S+P]++))); for(i=1,#v,if(v[i]>r,r=v[i];print1(i", "))
%Y Cf. A238403, A087053, A238397.
%K nonn
%O 1,1
%A _Charles R Greathouse IV_, Feb 26 2014
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