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 A271787 Integers n that are the sum of two nonzero squares while n*(n+1) is not. 0
 2, 5, 10, 13, 18, 20, 26, 29, 32, 34, 37, 41, 45, 50, 53, 58, 61, 65, 68, 74, 82, 85, 90, 98, 101, 104, 106, 109, 113, 117, 122, 125, 128, 130, 137, 146, 149, 153, 157, 160, 162, 164, 170, 173, 178, 181, 185, 194, 197, 200, 202, 205, 208, 212, 218, 221, 226, 229, 234, 242, 245, 250, 257, 261 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Values of a^2 + b^2 such that (a^2 + b^2)^2 + a^2 + b^2 is not of the form x^2 + y^2 where a, b, x, y are nonzero integers. LINKS EXAMPLE 5 is a term because 5 = 1^2 + 2^2 and 5^2 + 5 = 30 is not a member of A000404. MATHEMATICA Select[Range@ 270, Length@ First@ # >= 1 && Last@ # == {} &[PowersRepresentations[#, 2, 2] /. {0, _} -> Nothing & /@ {#, # (# + 1)} &@ #] &] (* Michael De Vlieger, Apr 14 2016 *) PROG (PARI) isA000404(n) = {for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2))} for(n=1, 1e3, if(!isA000404(n*(n+1)) && isA000404(n), print1(n, ", "))); CROSSREFS Cf. A000404, A002378. Sequence in context: A031396 A003814 A003654 * A047617 A190437 A190249 Adjacent sequences:  A271784 A271785 A271786 * A271788 A271789 A271790 KEYWORD nonn,easy AUTHOR Altug Alkan, Apr 14 2016 STATUS approved

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Last modified January 27 12:01 EST 2020. Contains 331295 sequences. (Running on oeis4.)