A057098 Shortest side of a Pythagorean triangle (ordered by the product of the sides).

3, 6, 5, 9, 8, 12, 7, 10, 15, 20, 18, 9, 12, 16, 21, 15, 24, 14, 11, 27, 20, 24, 30, 16, 28, 33, 13, 40, 25, 36, 21, 18, 33, 24, 32, 39, 42, 30, 15, 48, 20, 45, 36, 48, 40, 35, 28, 39, 51, 22, 60, 54, 17, 27, 40, 57, 36, 48, 65, 60, 24, 32, 35, 56, 63, 45, 60, 19, 66, 44, 56

Offset

1,1

Links

Table of n, a(n) for n=1..71.

Formula

a(n) =A057096(n)/(A057099(n)*A057100(n)) =sqrt(A057100(n)^2-A057099(n)^2)

Example

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

Mathematica

maxShortLeg = 66; terms = 71;
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, 1]] (* Jean-François Alcover, Nov 21 2019 *)

Crossrefs

Cf. A009004, A009005, A046083, A057096.

Sequence in context: A046128 A342222 A331164 * A053628 A334717 A334753

Adjacent sequences: A057095 A057096 A057097 * A057099 A057100 A057101

Keyword

nonn

Author

Henry Bottomley, Aug 01 2000

Status

approved