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A007969
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Rectangular numbers.
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11
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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
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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))=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]
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LINKS
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Table of n, a(n) for n=1..66.
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 + 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 *)
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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J. H. Conway
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STATUS
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approved
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