

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
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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]](* JeanFrançois 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 JeanFrançois Alcover, Jun 26 2012


STATUS

approved



