Let P be the set of prime numbers and P(n)denote the largest prime factor of integer n>1.Write C3={p1p2p3:pi∈P(i=1,2,3),pi=pj(i=j)},B3={p1p2p3:pi∈P(i=1,2,3),p1=p2 or p1=p3 or p2=p3,but not p1=p2=p3}.For n=p1p2p3...Let P be the set of prime numbers and P(n)denote the largest prime factor of integer n>1.Write C3={p1p2p3:pi∈P(i=1,2,3),pi=pj(i=j)},B3={p1p2p3:pi∈P(i=1,2,3),p1=p2 or p1=p3 or p2=p3,but not p1=p2=p3}.For n=p1p2p3∈C3∪B3,we define the w function byω(n)=P(p1+p2)P(p1+p3)P(p2+p3).If there is m∈S-C3∪B3 such thatω(m)=n,then we call m S-parent of n.We shall prove that there are infinitely many elements of C3 which have enough C3-parents and that there are infinitely many elements of B3 which have enough C3-parents.We shall also prove that there are infinitely many elements of B3 which have enough B3-parents.展开更多
文摘Let P be the set of prime numbers and P(n)denote the largest prime factor of integer n>1.Write C3={p1p2p3:pi∈P(i=1,2,3),pi=pj(i=j)},B3={p1p2p3:pi∈P(i=1,2,3),p1=p2 or p1=p3 or p2=p3,but not p1=p2=p3}.For n=p1p2p3∈C3∪B3,we define the w function byω(n)=P(p1+p2)P(p1+p3)P(p2+p3).If there is m∈S-C3∪B3 such thatω(m)=n,then we call m S-parent of n.We shall prove that there are infinitely many elements of C3 which have enough C3-parents and that there are infinitely many elements of B3 which have enough C3-parents.We shall also prove that there are infinitely many elements of B3 which have enough B3-parents.
