

A334587


Perimeters of primitive Heronian triangles whose longest side length is prime.


2



12, 30, 36, 40, 50, 60, 70, 76, 78, 80, 84, 90, 98, 100, 108, 112, 126, 128, 132, 144, 150, 152, 156, 160, 164, 176, 180, 182, 192, 196, 198, 200, 204, 208, 210, 216, 220, 224, 228, 230, 234, 236, 240, 242, 250, 256, 258, 260, 266, 270, 272, 286, 288, 300, 306, 320
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


LINKS

Table of n, a(n) for n=1..56.
Eric Weisstein's World of Mathematics, Heronian Triangle
Wikipedia, Heronian triangle
Wikipedia, Integer Triangle


FORMULA

Characteristic function: sign( Sum_{k=1..floor(n/3)} Sum_{i=k..floor((nk)/2)} sign(floor((i+k)/(nik+1))) * chi(sqrt((n/2)*(n/2i)*(n/2k)*(n/2(nik)))) * [gcd(i,k,nik) = 1] * c(nik) ), where chi is the integer characteristic, c is the prime characteristic (A010051) and [] is the Iverson bracket.


EXAMPLE

a(1) = 12; there is one primitive Heronian triangle with a perimeter of 12 whose longest side length is prime, which is [3,4,5].
a(4) = 40; there is one primitive Heronian triangle with a perimeter of 40 whose longest side length is prime, [8,15,17].


CROSSREFS

Cf. A010051, A096468, A334584, A334586.
Sequence in context: A335149 A050689 A144565 * A329947 A115912 A083096
Adjacent sequences: A334584 A334585 A334586 * A334588 A334589 A334590


KEYWORD

nonn


AUTHOR

Wesley Ivan Hurt, May 06 2020


STATUS

approved



