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A308224 Sum of the largest sides of all integer-sided triangles with perimeter n whose side lengths are mutually coprime. 1
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 7, 7, 0, 15, 0, 17, 9, 9, 11, 53, 11, 21, 37, 60, 26, 103, 13, 68, 28, 74, 49, 193, 34, 115, 106, 210, 74, 291, 76, 227, 97, 214, 107, 464, 132, 345, 205, 414, 117, 592, 198, 488, 223, 454, 214, 1037, 274, 591, 491 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

LINKS

Table of n, a(n) for n=1..63.

Wikipedia, Integer Triangle

FORMULA

a(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] * (n-i-k), where [] is the Iverson Bracket.

MATHEMATICA

Table[Sum[Sum[(n - i - k)*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. A308223.

Sequence in context: A261852 A254293 A263496 * A200630 A198225 A256929

Adjacent sequences:  A308221 A308222 A308223 * A308225 A308226 A308227

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 16 2019

STATUS

approved

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Last modified November 30 20:17 EST 2021. Contains 349425 sequences. (Running on oeis4.)