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A386418 a(n) is the number of nondegenerate triangles whose sides are distinct divisors of A386417(n).

%I A386418 #5 Aug 04 2025 21:28:57
%S A386418 2,1,5,4,6,4,2,8,3,23,1,3,19,8,14,1,17,11,1,2,3,10,2,7,57,14,1,11,13,
%T A386418 37,9,2,8,12,1,45,4,79,3,3,14,2,7,9,5,3,45,35,11,12,4,6,1,106,62,2,8,
%U A386418 33,1,34,3,4,41,1,3,57,4,3,50,2,6,7,25,12,16,14,30
%N A386418 a(n) is the number of nondegenerate triangles whose sides are distinct divisors of A386417(n).
%H A386418 Felix Huber, <a href="/A386418/b386418.txt">Table of n, a(n) for n = 1..10000</a>
%e A386418 a(1) = 2 because there are exactly the 2 triangles (2, 3, 4) and (3, 4, 6) whose sides are distinct divisors of A386417(1) = 12.
%p A386418 A386418:=proc(n)
%p A386418     option remember;
%p A386418     local a,k,i;
%p A386418     if n=1 then
%p A386418         [12,2]
%p A386418     else
%p A386418         for k from procname(n-1)[1]+1 do
%p A386418             a:=0;
%p A386418             for i in combinat[choose](NumberTheory:-Divisors(k),3) do
%p A386418                 if i[3]<i[1]+i[2] then
%p A386418                     a:=a+1
%p A386418                 fi
%p A386418             od;
%p A386418             if a>0 then
%p A386418                 return [k,a]
%p A386418             fi
%p A386418         od
%p A386418     fi;
%p A386418 end proc;
%p A386418 seq(A386417(n)[2],n=1..77);
%Y A386418 Cf. A027750, A378820, A386417.
%K A386418 nonn
%O A386418 1,1
%A A386418 _Felix Huber_, Jul 28 2025