A057099 Middle side of a Pythagorean triangle (ordered by the product of the sides).

4, 8, 12, 12, 15, 16, 24, 24, 20, 21, 24, 40, 35, 30, 28, 36, 32, 48, 60, 36, 48, 45, 40, 63, 45, 44, 84, 42, 60, 48, 72, 80, 56, 70, 60, 52, 56, 72, 112, 55, 99, 60, 77, 64, 75, 84, 96, 80, 68, 120, 63, 72, 144, 120, 96, 76, 105, 90, 72, 80, 143, 126, 120, 90, 84, 108, 91

Offset

1,1

Links

Table of n, a(n) for n=1..67.

Formula

a(n) =A057096(n)/(A057098(n)*A057100(n)) =sqrt(A057100(n)^2-A057098(n)^2)

Example

a(1)=4 since 3*4*5=60 is smallest possible positive product

Mathematica

maxShortLeg = 66; terms = 67;
r[a_] := {a, b, c} /. {ToRules[Reduce[a <= b < c && a^2+b^2 == c^2, {b, c}, Integers]]};
abc = r /@ Complement[Range[maxShortLeg], {1, 2, 4}] // Flatten[#, 1]&;
SortBy[abc, Times @@ # &][[;; terms, 2]] (* Jean-François Alcover, Nov 21 2019 *)

Crossrefs

Cf. A009012, A009023, A046084, A057096.

Sequence in context: A009012 A046084 A350058 * A334718 A334755 A333597

Adjacent sequences: A057096 A057097 A057098 * A057100 A057101 A057102

Keyword

nonn

Author

Henry Bottomley, Aug 01 2000

Status

approved