

A343892


Side b of integersided 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.


7



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
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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 proposed 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 3115 < 21 < 31+15.


MAPLE

for a from 4 to 200 do
for b from floor(a/2)+1 to a1 do
c := a*b/(2*ba);
if c=floor(c) and igcd(a, b, c)=1 and cb<a then print(b); end if;
end do;
end do;


CROSSREFS

Cf. A343891 (triples), A020883 (side a), A343893 (side c), A343894 (perimeter).
Cf. A020890 (sides b ordered).
Sequence in context: A283770 A088338 A020890 * A317671 A031453 A179203
Adjacent sequences: A343889 A343890 A343891 * A343893 A343894 A343895


KEYWORD

nonn


AUTHOR

Bernard Schott, May 06 2021


STATUS

approved



