

A308308


Number of integersided triangles with perimeter n and at least one pair of side lengths that are not coprime.


0



0, 0, 0, 0, 1, 1, 2, 1, 3, 2, 4, 2, 5, 4, 6, 4, 8, 5, 10, 6, 11, 9, 13, 7, 15, 12, 16, 11, 19, 11, 23, 16, 25, 19, 27, 15, 31, 23, 31, 21, 36, 21, 40, 28, 43, 33, 47, 26, 50, 36, 52, 38, 60, 36, 62, 45, 66, 52, 72, 36, 75, 58, 74, 56, 84, 49, 91, 64, 93, 65
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OFFSET

1,7


LINKS

Table of n, a(n) for n=1..70.
Wikipedia, Integer Triangle


FORMULA

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((nk)/2)} sign(floor((i+k)/(nik+1))) * (1  [gcd(i,k) * gcd(i,nik) * gcd(k,nik) = 1]), where [] is the Iverson bracket.
a(n) = A005044(n)  A308074(n).


MATHEMATICA

Table[Sum[Sum[(1  KroneckerDelta[GCD[i, k]*GCD[i, n  i  k]*GCD[k, n  i  k], 1])*Sign[Floor[(i + k)/(n  i  k + 1)]], {i, k, Floor[(n  k)/2]}], {k, Floor[n/3]}], {n, 100}]


CROSSREFS

Cf. A005044, A308074.
Sequence in context: A130722 A308307 A147541 * A024162 A334677 A179080
Adjacent sequences: A308305 A308306 A308307 * A308309 A308310 A308311


KEYWORD

nonn


AUTHOR

Wesley Ivan Hurt, May 19 2019


STATUS

approved



