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A070105
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Number of integer triangles with perimeter n and prime side lengths which are obtuse and scalene.
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5
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 0, 0, 3, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 3, 0, 1, 0, 3, 0, 4, 0, 3, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 3, 0, 1, 0, 5, 0, 4, 0, 5, 0, 5, 0
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OFFSET
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1,35
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COMMENTS
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LINKS
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MAPLE
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f:= proc(n) local a, b, q, bmin, bmax, t;
t:= 0;
if n::even then return 0 fi;
for a from 1 to n/3 by 2 do
if not isprime(a) then next fi;
bmin:= max(a+1, (n+1)/2-a); if bmin::even then bmin:= bmin+1 fi;
q:= (n^2-2*n*a)/(2*(n-a));
if q::integer then bmax:= min((n-a)/2, q-1) else bmax:= min((n-a)/2, floor(q)) fi;
t:= t + nops(select(b -> isprime(b) and isprime(n-a-b), [seq(b, b=bmin .. bmax, 2)]))
od;
t
end proc:
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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