A063665 - OEIS

A063665

Number of ways 1/n can be written as 1/x^2 + 1/y^2 with y >= x >= 1.

0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0

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OFFSET

1,98

COMMENTS

Number of ordered pairs (x,y), with n = (x^2)(y^2)/(x^2 + y^2) and y >= x > 0. - Antti Karttunen, Nov 07 2018

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

EXAMPLE

a(90)=1 since 1/90 = 1/10^2 + 1/30^2

a(98)=2 since 1/98 = 1/10^2 + 1/70^2 = 1/14^2 + 1/14^2.

a(14400) = 3 since 1/14400 = 1/130^2 + 1/312^2 = 1/136^2 + 1/255^2 = 1/150^2 + 1/200^2. - Antti Karttunen, Nov 07 2018

PROG

(PARI) A063665(n) = { my(s=0); for(x=1, n, for(y=x, n, if((n*(x*x+y*y)) == (x*x*y*y), s++))); (s); }; \\ Antti Karttunen, Nov 07 2018

(PARI) A063665(n) = { my(s=0, y); for(x=sqrtint(n), n, my(x2=x*x); if((x2>n)&&issquare((n*x2)/(x2-n), &y)&&(1==denominator(y))&&(y>=x), s++)); (s); }; \\ Antti Karttunen, Nov 07 2018

CROSSREFS

Cf. A000161, A025426, A018892, A063664.

Sequence in context: A102683 A122840 A083919 * A276306 A340851 A130779

Adjacent sequences: A063662 A063663 A063664 * A063666 A063667 A063668

KEYWORD

nonn

AUTHOR

Henry Bottomley, Jul 25 2001

EXTENSIONS

Definition clarified by Antti Karttunen, Nov 07 2018

STATUS

approved