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A232437 Numbers whose square is expressible in only one way as x^2+xy+y^2, with x and y > 0. 5


%S 7,13,14,19,21,26,28,31,35,37,38,39,42,43,52,56,57,61,62,63,65,67,70,

%T 73,74,76,77,78,79,84,86,93,95,97,103,104,105,109,111,112,114,117,119,

%U 122,124,126,127,129,130,134,139,140,143,146,148,151,152,154,155,156,157,158,161

%N Numbers whose square is expressible in only one way as x^2+xy+y^2, with x and y > 0.

%C Analog of A084645 for 120-degree angle triangles with integer sides.

%C Numbers with exactly one prime divisor of the form 6k+1 with multiplicity one.

%C Primitive elements of A050931.

%H <a href="/index/Aa#A2">Index entries for sequences related to A2 = hexagonal = triangular lattice</a>

%F Terms are obtained by the products A230780(k)*A002476(p) for k, p > 0, ordered by increasing values.

%e a(1) = 7 as 7^2 = 3^2 + 3*5 + 5^2.

%t selQ[1] = False; selQ[n_] := Module[{f = FactorInteger[n]}, Count[f, {p_, 1} /; Mod[p, 6] == 1] == 1]; Select[Range[200], selQ] (* _Jean-François Alcover_, Nov 25 2013, after comments *)

%Y Cf. A002476, A050931, A230780, A232436 (subsequence).

%Y Cf. A084645, A232437, A248599, A254063, A254064.

%K nonn

%O 1,1

%A _Jean-Christophe Hervé_, Nov 24 2013

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Last modified December 7 03:00 EST 2019. Contains 329836 sequences. (Running on oeis4.)