A237992 Numbers which can be decomposed as p*q + q*r + r*p (where p < q < r are distinct primes) in more ways than any smaller number.
31, 71, 151, 191, 311, 1031, 1991, 3191, 5351, 5591, 10391, 15791, 17111, 27191, 31391, 35591, 42311, 50951, 70391, 93551, 107159, 117911, 119831, 126551, 166871, 180311, 191831, 216191, 255191, 259871, 327071, 366791, 435431, 465911, 514751, 576551, 599231, 631991
Offset: 1
Keywords
Examples
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.
Programs
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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", ")))
Comments