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A308223 Sum of the smallest side lengths 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, 3, 0, 0, 3, 4, 0, 8, 0, 9, 5, 5, 5, 25, 5, 14, 15, 31, 12, 50, 7, 33, 16, 39, 19, 86, 16, 57, 46, 99, 32, 142, 34, 116, 49, 108, 47, 208, 56, 172, 91, 189, 57, 274, 86, 232, 109, 225, 92, 463, 118, 294, 195, 378, 150, 562 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

LINKS

Table of n, a(n) for n=1..66.

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] * k, where [] is the Iverson Bracket.

MATHEMATICA

Table[Sum[Sum[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. A308074.

Sequence in context: A279168 A111787 A200524 * A222328 A222402 A222522

Adjacent sequences:  A308220 A308221 A308222 * A308224 A308225 A308226

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 16 2019

STATUS

approved

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Last modified February 20 04:32 EST 2020. Contains 332063 sequences. (Running on oeis4.)