

A308061


Number of integersided triangles with perimeter n whose side lengths are squarefree.


5



0, 0, 1, 0, 1, 1, 2, 1, 1, 0, 2, 1, 3, 2, 5, 3, 3, 2, 2, 1, 3, 3, 6, 4, 3, 2, 6, 4, 7, 7, 11, 8, 8, 6, 11, 8, 9, 6, 13, 9, 10, 6, 13, 9, 16, 12, 20, 15, 17, 12, 15, 10, 16, 14, 15, 11, 12, 10, 16, 12, 18, 18, 25, 19, 21, 19, 26, 19, 29, 27, 35, 27, 29, 27
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OFFSET

1,7


LINKS

Table of n, a(n) for n=1..74.


FORMULA

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((nk)/2)} sign(floor((i+k)/(nik+1))) * mu(i)^2 * mu(k)^2 * mu(nik)^2, where mu is the Möbius function (A008683).


MATHEMATICA

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


CROSSREFS

Cf. A005044, A008683.
Sequence in context: A029375 A071462 A101979 * A060582 A060450 A180918
Adjacent sequences: A308058 A308059 A308060 * A308062 A308063 A308064


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, May 10 2019


STATUS

approved



