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 A274794 Numbers n such that n^3 is the sum of two triangular numbers in exactly one way. 0
 0, 1, 3, 4, 7, 9, 10, 19, 24, 25, 34, 37, 39, 42, 49, 54, 55, 72, 73, 78, 85, 87, 93, 94, 102, 108, 109, 118, 138, 142, 147, 157, 160, 165, 168, 175, 192, 195, 202, 210, 214, 220, 228, 232, 243, 247, 249, 250, 252, 253, 258, 267, 273, 274, 279, 289, 297, 312, 333 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A115104 is a subsequence. Terms such that 4*n^3 + 1 is not prime are 24, 337, 457, 750, 840, 1015, ... LINKS EXAMPLE 3 is a term because 3^3 = 27 = 6 + 21. MATHEMATICA Select[Range@ 333, Length[PowersRepresentations[4 #^3 + 1, 2, 2]] == 1 &] (* after Ant King at A052343, or *) nn = 20; t = (#^2 + #)/2 & /@ Range[0, nn^3]; Select[Range[0, nn], Function[n, Count[Transpose@ {#, n^3 - #} &@ Range[0, Floor[n^3/2]], k_ /; Times @@ Boole@ Map[MemberQ[t, #] &, k] == 1] == 1]] (* Michael De Vlieger, Jul 07 2016 *) PROG (PARI) a052343(n) = sum(i=0, (sqrtint(4*n + 1) - 1)\2, issquare(n - i - i^2)); lista(nn) = for(n=0, nn, if(a052343(n^3) == 1, print1(n, ", "))); CROSSREFS Cf. A000217, A000578, A020756, A052343, A115104, A119345. Sequence in context: A212013 A256761 A039579 * A115104 A095043 A019990 Adjacent sequences:  A274791 A274792 A274793 * A274795 A274796 A274797 KEYWORD nonn AUTHOR Altug Alkan, Jul 07 2016 STATUS approved

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Last modified January 24 10:42 EST 2020. Contains 331193 sequences. (Running on oeis4.)