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A007969 Rectangular numbers. 11
2, 5, 6, 10, 12, 13, 14, 17, 18, 20, 21, 22, 26, 28, 29, 30, 33, 34, 37, 38, 39, 41, 42, 44, 45, 46, 50, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 65, 66, 68, 69, 70, 72, 73, 74, 76, 77, 78, 82, 84, 85, 86, 89, 90, 92, 93, 94, 95, 97, 98, 101, 102, 105, 106, 108, 109 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A000037; A007968(a(n))=1; A002144 is a subsequence;

A191854(n) = A007966(a(n)); A191855(n) = A007967(a(n));

a(n) = A191854(n)*A191855(n). [Reinhard Zumkeller, Jun 18 2011]

LINKS

Table of n, a(n) for n=1..66.

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 + 1 == 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[ c > 1 && (r0 = r[b, c]) =!= False, {x0, y0} = {x, y} /. ToRules[r0]; Throw[n]]; If[ b > 1 && (r0 = r[c, b]) =!= False, {x0, y0} = {x, y} /. ToRules[r0]; Throw[n]], {bc, Union[Sort[{#, n/#}] & /@ Divisors[n]]} ]]]; A007969 = Reap[ Table[ If[f[n] =!= Null, Print[f[n]]; Sow[f[n]]], {n, 1, 109}] ][[2, 1]] (* Jean-François Alcover, Jun 26 2012 *)

CROSSREFS

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

Sequence in context: A238096 A064572 A032399 * A187902 A187231 A162340

Adjacent sequences:  A007966 A007967 A007968 * A007970 A007971 A007972

KEYWORD

nonn

AUTHOR

J. H. Conway

STATUS

approved

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Last modified April 20 19:37 EDT 2014. Contains 240820 sequences.