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

8, 12, 18, 27, 45, 50, 75, 98, 105, 125, 147, 175, 242, 245, 338, 343, 363, 385, 429, 507, 539, 578, 605, 637, 715, 722, 845, 847, 867, 969, 1001, 1058, 1083, 1105, 1183, 1309, 1331, 1445, 1547, 1573, 1587, 1615, 1682, 1729, 1805, 1859, 1922, 2023, 2057, 2185, 2197

Offset: 1

Author

Felix Huber, Dec 24 2024

Keywords

• nonn

Comments

Subsequence of A014612 and of A145784.

Numbers that are the product of exactly three (not necessarily distinct) primes and these primes are sides of a degenerate triangle are in A071142.

Examples

			12 = 2*2*3 is in the sequence because 2 + 2 > 3.
20 = 2*2*5 is not in the sequence because 2 + 2 < 5.
30 = 2*3*5 is not in the sequence because 2 + 3 = 5.
		

Links

• Felix Huber, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001222, A014612, A070088, A071142, A145784, A306678, A366398, A378819.

Programs

Maple

A379033:=proc(n)
   option remember;
   local a,i,j,P;
   if n=1 then
      8
   else
      for a from procname(n-1)+1 do
         P:=[];
         if NumberTheory:-Omega(a)=3 then
            for i in ifactors(a)[2] do
               j:=0;
               while jP[3] then
               return a
            fi
         fi
      od
   fi	
end proc;
seq(A379033(n),n=1..51);