A265189 -id:A265189 - cp's OEIS frontend

A280679 The radii (a, b, c) of three primitive mutually tangent circles all touching the same straight line, with a > b > c.

36, 9, 4, 144, 16, 9, 225, 100, 36, 400, 25, 16, 784, 441, 144, 900, 36, 25, 1225, 196, 100, 1600, 576, 225, 1764, 49, 36, 2025, 1296, 400, 3136, 64, 49, 3969, 324, 196, 4356, 3025, 900, 4900, 900, 441, 5184, 81, 64, 5929, 1936, 784, 7056, 3600, 1225

Offset: 1

Colin Barker, Jan 07 2017

Colin Barker, Table of n, a(n) for n = 1..3000
Eric Weisstein's World of Mathematics, Tangent Circles

Cf. A265189, A280680.

a280679(amax) = {
  my(L=List());
  for(a=1, amax,
    for(b=1, a-1,
      c=(1/(1/a + 1/b))^2;
      if(type(c)=="t_INT" && gcd([a^2,b^2,c])==1,
        listput(L, [a^2,b^2,c])
      )
    )
  );
  Vec(L)
}
concat(a280679(100))

The first few triples are [36, 9, 4], [144, 16, 9], [225, 100, 36], [400, 25, 16].

A280680 The square roots of the radii (a, b, c) of three primitive mutually tangent circles all touching the same straight line, with a > b > c.

Original entry on oeis.org

6, 3, 2, 12, 4, 3, 15, 10, 6, 20, 5, 4, 28, 21, 12, 30, 6, 5, 35, 14, 10, 40, 24, 15, 42, 7, 6, 45, 36, 20, 56, 8, 7, 63, 18, 14, 66, 55, 30, 70, 30, 21, 72, 9, 8, 77, 44, 28, 84, 60, 35, 88, 33, 24, 90, 10, 9, 91, 78, 42, 99, 22, 18, 104, 65, 40

Offset: 1

Colin Barker, Jan 07 2017

			The first few triples are [6, 3, 2], [12, 4, 3], [15, 10, 6], [20, 5, 4].

Colin Barker, Table of n, a(n) for n = 1..3000
Eric Weisstein's World of Mathematics, Tangent Circles

Cf. A106430, A246429, A247372, A265189, A280679.

a280680(amax) = {
  my(L=List());
  for(a=1, amax,
    for(b=1, a-1,
      c=(1/(1/a + 1/b))^2;
      if(type(c)=="t_INT" && gcd([a^2,b^2,c])==1,
        listput(L, [a,b,sqrtint(c)])
      )
    )
  );
  Vec(L)
}
concat(a280680(100))

cp's OEIS Frontend

A280679 The radii (a, b, c) of three primitive mutually tangent circles all touching the same straight line, with a > b > c.

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