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 A063665 Number of ways 1/n can be written as 1/x^2 + 1/y^2 with y >= x >= 1. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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 A072507 A340851 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

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Last modified May 18 08:21 EDT 2021. Contains 343995 sequences. (Running on oeis4.)