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A007970 Rhombic numbers. 10
3, 7, 8, 11, 15, 19, 23, 24, 27, 31, 32, 35, 40, 43, 47, 48, 51, 59, 63, 67, 71, 75, 79, 80, 83, 87, 88, 91, 96, 99, 103, 104, 107, 115, 119, 120, 123, 127, 128, 131, 135, 136, 139, 143, 151, 152, 159, 160, 163, 167, 168, 171, 175, 176, 179 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A000037; A007968(a(n))=2; A002145 is a subsequence;

A191856(n) = A007966(a(n)); A191857(n) = A007967(a(n));

a(n) = A191856(n)*A191857(n). [Reinhard Zumkeller, Jun 18 2011]

LINKS

Table of n, a(n) for n=1..55.

J. H. Conway, On Happy Factorizations, J. Integer Sequences, Vol. 1, 1998, #1.

MATHEMATICA

r[b_, c_] := (red = Reduce[x > 0 && y > 0 && b*x^2 + 2 == c*y^2, {x, y}, Integers] /. C[1] -> 1 // Simplify; If[Head[red] === Or, First[red], red]); f[n_] := f[n] = If[! IntegerQ[Sqrt[n]], Catch[Do[{b, c} = bc; If[ (r0 = r[b, c]) =!= False, {x0, y0} = {x, y} /. ToRules[r0]; If[OddQ[x0] && OddQ[y0], Throw[n]]]; If[ (r0 = r[c, b]) =!= False, {x0, y0} = {x, y} /. ToRules[r0]; If[OddQ[x0] && OddQ[y0], Throw[n]]], {bc, Union[Sort[{#, n/#}] & /@ Divisors[n]]} ]]]; A007970 = Reap[ Table[ If[f[n] =!= Null, Print[f[n]]; Sow[f[n]]], {n, 1, 180}] ][[2, 1]](* Jean-François Alcover, Jun 26 2012 *)

CROSSREFS

Every number belongs to exactly one of A000290, A007969, A007970.

Sequence in context: A078466 A047528 A069122 * A134258 A028972 A153030

Adjacent sequences:  A007967 A007968 A007969 * A007971 A007972 A007973

KEYWORD

nonn

AUTHOR

J. H. Conway

EXTENSIONS

159 and 175 inserted by Jean-François Alcover, Jun 26 2012

STATUS

approved

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Last modified August 31 06:30 EDT 2014. Contains 246235 sequences.