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A307828 Number of integer-sided triangles with perimeter n whose smallest side-length divides n.

%I A307828 #75 Mar 17 2025 03:40:05
%S A307828 0,0,1,0,1,1,1,1,2,1,1,3,1,1,4,3,1,3,1,5,4,1,1,8,4,1,4,6,1,8,1,7,4,1,
%T A307828 8,12,1,1,4,14,1,9,1,8,12,1,1,18,5,8,4,9,1,10,10,17,4,1,1,28,1,1,13,
%U A307828 15,11,11,1,11,4,18,1,31,1,1,15,12,11,12,1,32
%N A307828 Number of integer-sided triangles with perimeter n whose smallest side-length divides n.
%H A307828 Antti Karttunen, <a href="/A307828/b307828.txt">Table of n, a(n) for n = 1..10220</a>
%H A307828 Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>
%F A307828 a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1)) * (1 - ceiling(n/k) + floor(n/k))).
%t A307828 Table[Sum[Sum[(1 - Ceiling[n/k] + Floor[n/k]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
%o A307828 (PARI) A307828(n) = sum(k=1, n\3, sum(i=k, (n-k)\2, sign(floor((i+k)/(n-i-k+1)) * (1 - ceil(n/k) + floor(n/k))))); \\ _Antti Karttunen_, Dec 05 2021
%Y A307828 Cf. A005044.
%K A307828 nonn
%O A307828 1,9
%A A307828 _Wesley Ivan Hurt_, May 15 2019