VOOZH about

URL: https://oeis.org/A308229

⇱ A308229 - OEIS

login
A308229
Sum of the perimeters of all triangles with perimeter n whose side lengths are mutually coprime.
0
0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 15, 16, 0, 36, 0, 40, 21, 22, 23, 120, 25, 52, 81, 140, 58, 240, 31, 160, 66, 170, 105, 432, 74, 266, 234, 480, 164, 672, 172, 528, 225, 506, 235, 1056, 294, 800, 459, 936, 265, 1350, 440, 1120, 513, 1044, 472, 2340
OFFSET
1,3
FORMULA
a(n) = n * A308074(n).
a(n) = n * Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * [gcd(i,k) * gcd(i,n-i-k) * gcd(k,n-i-k) = 1], where [] is the Iverson Bracket.
MATHEMATICA
Table[n*Sum[Sum[Floor[1/(GCD[i, k]*GCD[i, n - i - k]*GCD[k, n - i - k])]*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
CROSSREFS
Cf. A308074.
Sequence in context: A062535 A063667 A171063 * A318673 A151795 A375199
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 16 2019
STATUS
approved