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A386417 Numbers k for which there exists at least one nondegenerate triangle with sides that are distinct divisors of k.

%I A386417 #8 Aug 04 2025 21:27:18
%S A386417 12,20,24,30,36,40,42,48,56,60,63,70,72,80,84,88,90,96,99,100,105,108,
%T A386417 110,112,120,126,130,132,140,144,150,154,156,160,165,168,176,180,182,
%U A386417 189,192,195,198,200,204,208,210,216,220,224,228,234,238,240,252,255,260
%N A386417 Numbers k for which there exists at least one nondegenerate triangle with sides that are distinct divisors of k.
%C A386417 If k is a term, then m*k is also a term for all positive integers m.
%H A386417 Felix Huber, <a href="/A386417/b386417.txt">Table of n, a(n) for n = 1..10000</a>
%e A386417 12 is a term because the sides of the nondegenerate triangles (2, 3, 4) and (3, 4, 6) are divisors of 12.
%p A386417 A386417:=proc(n)
%p A386417     option remember;
%p A386417     local k,i;
%p A386417     if n=1 then
%p A386417         12
%p A386417     else
%p A386417         for k from procname(n-1)+1 do
%p A386417             for i in combinat[choose](NumberTheory:-Divisors(k),3) do
%p A386417                 if i[3]<i[1]+i[2] then
%p A386417                     return k
%p A386417                 fi
%p A386417             od
%p A386417         od
%p A386417     fi;
%p A386417 end proc;
%p A386417 seq(A386417(n),n=1..25);
%Y A386417 Cf. A027750, A378820, A386418.
%K A386417 nonn
%O A386417 1,1
%A A386417 _Felix Huber_, Jul 28 2025