A343892 - OEIS

A343892

Side b 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.

3, 10, 12, 15, 21, 30, 36, 35, 40, 44, 55, 56, 52, 63, 65, 78, 70, 90, 77, 105, 99, 85, 102, 119, 132, 136, 117, 114, 143, 133, 126, 152, 171, 154, 182, 168, 165, 210, 195, 161, 176, 184, 208, 207, 187, 240, 230, 253, 200, 221, 198, 255, 225, 234, 216, 275, 300, 306, 247, 270

(list; graph; refs; listen; history; text; internal format)

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(7) = 36 > a(8) = 35, but, these sides b are listed in increasing order in A020890.

The first term appearing twice is 330 and corresponds to triples (435, 330, 638) and (460, 330, 759), the second one is 462 and corresponds to triples (483, 462, 506) and (532, 462, 627).

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, 2).

EXAMPLE

a(4) = 15, because the fourth triple is (21, 15, 35) with side b = 15, satisfying 1/15 = 2/21 - 1/35 and 31-15 < 21 < 31+15.

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(b); end if;