A343893 Side c of integer-sided primitive triangles (a, b, c) where side a is the harmonic mean of the 2 other sides b and c, i.e., 2/a = 1/b + 1/c with b < a < c.

6, 15, 20, 35, 28, 42, 45, 63, 88, 77, 66, 72, 117, 99, 104, 91, 130, 110, 165, 120, 143, 204, 187, 170, 156, 153, 221, 247, 195, 228, 266, 209, 190, 238, 210, 273, 285, 231, 255, 368, 336, 345, 304, 322, 391, 272, 299, 276, 425, 357, 450, 323, 400, 414, 513, 350, 325, 342, 475, 459

Offset

1,1

Comments

The triples (a, b, c) are displayed in increasing order of side a, and if sides a coincide then in increasing order of the side b.

The sequence is not increasing because a(4) = 35 > a(5) = 28, but, these sides c are listed in increasing order in A020886.

For the corresponding primitive triples and miscellaneous properties and references, see A343891.

Links

Table of n, a(n) for n=1..60.

Formula

a(n) = A343891(n, 3).

Example

a(3) = 20, because the third triple is (15, 12, 20) with side c = 20, satisfying 1/20 = 2/15 - 1/12 and 15-12 < 20 < 15+12.

Maple

for a from 4 to 200 do
for b from floor(a/2)+1 to a-1 do
c := a*b/(2*b-a);
if c=floor(c) and igcd(a, b, c)=1 and c-b<a then print(c); end if;
end do;
end do;

Crossrefs

Cf. A343891 (triples), A020883 (side a), A343892 (side b), A343894 (perimeter).

Cf. A020886 (sides c ordered).

Sequence in context: A094183 A196394 A162693 * A056901 A208542 A012412

Adjacent sequences: A343890 A343891 A343892 * A343894 A343895 A343896

Keyword

nonn

Author

Bernard Schott, May 06 2021

Status

approved