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

1,3

LINKS

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

Wikipedia, Integer Triangle

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 A008437

Adjacent sequences:  A308226 A308227 A308228 * A308230 A308231 A308232

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 16 2019

STATUS

approved

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Last modified September 27 22:36 EDT 2020. Contains 337388 sequences. (Running on oeis4.)