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 A025052 Numbers not of form ab + bc + ca for 1<=a<=b<=c (probably the list is complete). 21
 1, 2, 4, 6, 10, 18, 22, 30, 42, 58, 70, 78, 102, 130, 190, 210, 330, 462 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Subsequence of A000926. According to Borwein and Choi, if the Generalized Riemann Hypothesis is true, then this sequence has no larger terms, otherwise there may be one term greater than 10^11. - T. D. Noe, Apr 08 2004 Note that n+1 must be prime for all n in this sequence. - T. D. Noe, Apr 28 2004 Borwein and Choi prove (Theorem 6.2) that the equation N=xy+xz+yz has an integer solution x,y,z>0 if N contains a square factor and N is not 4 or 18. In the following simple proof explicit solutions are given. Let N=mn^2, m,n integer, m>0, n>1. If n3: x=6, y=n-3, z=n^2-4n+6. If n>m+1: if n=0 (mod m+1): x=m+1, y=m(m+1), z=m(n^2/(m+1)^2-1), if n=k (mod m+1), 0

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Last modified March 29 15:16 EDT 2020. Contains 333107 sequences. (Running on oeis4.)