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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
7, 13, 14, 19, 21, 26, 28, 31, 35, 37, 38, 39, 42, 43, 52, 56, 57, 61, 62, 63, 65, 67, 70, 73, 74, 76, 77, 78, 79, 84, 86, 93, 95, 97, 103, 104, 105, 109, 111, 112, 114, 117, 119, 122, 124, 126, 127, 129, 130, 134, 139, 140, 143, 146, 148, 151, 152, 154, 155, 156, 157, 158, 161 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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

Primitive elements of A050931.

LINKS

Table of n, a(n) for n=1..63.

Index entries for sequences related to A2 = hexagonal = triangular lattice

FORMULA

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

EXAMPLE

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

MATHEMATICA

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 *)

CROSSREFS

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

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

Sequence in context: A013651 A050931 A072864 * A275201 A274558 A120100

Adjacent sequences:  A232434 A232435 A232436 * A232438 A232439 A232440

KEYWORD

nonn

AUTHOR

Jean-Christophe Hervé, Nov 24 2013

STATUS

approved

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Last modified November 17 16:08 EST 2019. Contains 329241 sequences. (Running on oeis4.)