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A007970
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Rhombic numbers.
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10
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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
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OFFSET
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1,1
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COMMENTS
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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]
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LINKS
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Table of n, a(n) for n=1..55.
J. H. Conway, On Happy Factorizations, J. Integer Sequences, Vol. 1, 1998, #1.
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MATHEMATICA
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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 *)
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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J. H. Conway (conway(AT)math.princeton.edu)
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EXTENSIONS
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159 and 175 inserted by Jean-François Alcover, Jun 26 2012
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STATUS
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approved
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