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A379033 Numbers that are the product of exactly three (not necessarily distinct) primes and these primes are sides of a nondegenerate triangle.

%I A379033 #7 Dec 26 2024 20:06:35
%S A379033 8,12,18,27,45,50,75,98,105,125,147,175,242,245,338,343,363,385,429,
%T A379033 507,539,578,605,637,715,722,845,847,867,969,1001,1058,1083,1105,1183,
%U A379033 1309,1331,1445,1547,1573,1587,1615,1682,1729,1805,1859,1922,2023,2057,2185,2197
%N A379033 Numbers that are the product of exactly three (not necessarily distinct) primes and these primes are sides of a nondegenerate triangle.
%C A379033 Subsequence of A014612 and of A145784.
%C A379033 Numbers that are the product of exactly three (not necessarily distinct) primes and these primes are sides of a degenerate triangle are in A071142.
%H A379033 Felix Huber, <a href="/A379033/b379033.txt">Table of n, a(n) for n = 1..10000</a>
%e A379033 12 = 2*2*3 is in the sequence because 2 + 2 > 3.
%e A379033 20 = 2*2*5 is not in the sequence because 2 + 2 < 5.
%e A379033 30 = 2*3*5 is not in the sequence because 2 + 3 = 5.
%p A379033 A379033:=proc(n)
%p A379033    option remember;
%p A379033    local a,i,j,P;
%p A379033    if n=1 then
%p A379033       8
%p A379033    else
%p A379033       for a from procname(n-1)+1 do
%p A379033          P:=[];
%p A379033          if NumberTheory:-Omega(a)=3 then
%p A379033             for i in ifactors(a)[2] do
%p A379033                j:=0;
%p A379033                while j<i[2] do
%p A379033                   P:=[op(P),i[1]];
%p A379033                   j:=j+1;
%p A379033                od
%p A379033             od;
%p A379033             if P[1]+P[2]>P[3] then
%p A379033                return a
%p A379033             fi
%p A379033          fi
%p A379033       od
%p A379033    fi	
%p A379033 end proc;
%p A379033 seq(A379033(n),n=1..51);
%Y A379033 Cf. A000040, A001222, A014612, A070088, A071142, A145784, A306678, A366398, A378819.
%K A379033 nonn
%O A379033 1,1
%A A379033 _Felix Huber_, Dec 24 2024