OFFSET
1,3
COMMENTS
EXAMPLE
For n = 3 the a(3) = 2 solutions are (x,y) = (1,1) and (2,2).
For n = 7 the a(7) = 6 solutions are (x,y) = (1,2), (1,4), (2,4), (3,5), (3,6), (5,6).
MAPLE
a:=[];
for n from 1 to 140 do
c:=0;
for y from 1 to n-1 do
for x from 1 to y do
if gcd(y, n) = 1 and gcd(x, n) = 1 and gcd(x+y, n) = 1 and (1/x + 1/y - 1/(x+y)) mod n = 0 then c:=c+1; fi;
od: # od x
od: # od y
a:=[op(a), c];
od: # od n
a;
PROG
(Python)
from math import gcd
def A376202(n):
c = 0
for x in range(1, n):
if gcd(x, n) == 1:
for y in range(x, n):
if gcd(y, n)==gcd(z:=x+y, n)==1 and not (w:=z**2-x*y)//gcd(w, x*y*z)%n:
c += 1
return c # Chai Wah Wu, Oct 06 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Tom Duff and N. J. A. Sloane, Oct 06 2024
STATUS
approved