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

1,1

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.

Links

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

Example

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.

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 j<i[2] do
                  P:=[op(P), i[1]];
                  j:=j+1;
               od
            od;
            if P[1]+P[2]>P[3] then
               return a
            fi
         fi
      od
   fi	
end proc;
seq(A379033(n), n=1..51);

Crossrefs

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

Sequence in context: A120137 A274951 A364776 * A033477 A105936 A168670

Adjacent sequences: A379030 A379031 A379032 * A379034 A379035 A379037

Keyword

nonn,new

Author

Felix Huber, Dec 24 2024

Status

approved