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Revision History for A297968

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A297968

Number of solutions to x*y*(x+y)=n in coprime integers.
(history; published version)

#20 by Susanna Cuyler at Mon Apr 29 07:05:30 EDT 2019

STATUS

proposed

approved

#19 by Jean-François Alcover at Mon Apr 29 03:10:09 EDT 2019

STATUS

editing

proposed

#18 by Jean-François Alcover at Mon Apr 29 03:10:04 EDT 2019

MATHEMATICA

f[n_] := Module[{d, count, x, s, ys}, d = Divisors[n]; count = 0; Do[If[ IntegerQ[Sqrt[x^4 + 4n x]], s = Sqrt[x^4 + 4n x]; ys = Select[{-(s+x^2)/ (2x), (x^2-s)/(2x)}, IntegerQ[#] && GCD[#, x] == 1&]; count = count + Length[ys]], {x, Union[d, -d]}]; count]; Array[f, 200] (* Jean-François Alcover, Apr 29 2019, after Robert Israel *)

STATUS

approved

editing

#17 by OEIS Server at Thu Jan 11 02:40:37 EST 2018

LINKS

Robert Israel, <a href="/A297968/b297968_1.txt">Table of n, a(n) for n = 1..10000</a>

#16 by N. J. A. Sloane at Thu Jan 11 02:40:36 EST 2018

STATUS

proposed

approved

Discussion

Thu Jan 11

02:40

OEIS Server: Installed new b-file as b297968.txt.  Old b-file is now b297968_1.txt.

#15 by Robert Israel at Wed Jan 10 20:15:00 EST 2018

STATUS

editing

proposed

#14 by Robert Israel at Wed Jan 10 20:13:53 EST 2018

MAPLE

for x in d union map(`-`, d) do

Discussion

Wed Jan 10

20:15

Robert Israel: My program had a bug: it only counted positive x values.  Corrected now.

#13 by Robert Israel at Wed Jan 10 20:13:20 EST 2018

DATA

0, 2, 4, 0, 0, 0, 4, 6, 0, 0, 0, 0, 0, 4, 6, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 4, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 0, 0, 0, 0, 4, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0

LINKS

Robert Israel, <a href="/A297968/b297968_1.txt">Table of n, a(n) for n = 1..10000</a>

EXAMPLE

For n=6 the a(n)=6 solutions are (x,y) = (-3,1), (-3,2), (1,-3), (1,2), (2,1) and (2,-3).

STATUS

proposed

editing

#12 by Robert Israel at Wed Jan 10 20:02:57 EST 2018

STATUS

editing

proposed

#11 by Robert Israel at Wed Jan 10 20:02:54 EST 2018

COMMENTS

a(n)=0 if n is odd. - Robert Israel, Jan 10 2018

STATUS

proposed

editing