A379532 Ulam numbers that are products of exactly four distinct primes (or tetraprimes).

390, 546, 690, 798, 1155, 1230, 1770, 2010, 2090, 2418, 2618, 2814, 3090, 3290, 3390, 3930, 4326, 4370, 4470, 4578, 4602, 4641, 6110, 6870, 7170, 7490, 7735, 7930, 8294, 9834, 10110, 10545, 10738, 11102, 11346, 11390, 11454, 11622, 11715, 11886, 12270, 12441, 12470, 12570

Offset: 1

Author

Massimo Kofler, Dec 24 2024

Keywords

• nonn

Comments

Ulam numbers: a(1) = 1; a(2) = 2; for n>2, a(n) = least number > a(n-1) which is a unique sum of two distinct earlier terms.

Examples

			390 is a term because 390=2*3*5*13 is the product of 4 distinct primes and 390 is an Ulam number.
546 is a term because 546=2*3*7*13 is the product of 4 distinct primes and 546 is an Ulam number.
1155 is a term because 1155=3*5*7*11 is the product of 4 distinct primes and 1155 is an Ulam number.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..6826

Crossrefs

Intersection of A002858 and A046386.

Cf. A068820, A378795, A379162.

Programs

Maple

N:= 20000: # for terms <= N
U:= [1,2]: V:= Vector(N): V[3]:= 1: R:= NULL: count:= 0:
for i from 3 do
   for k from U[-1]+1 to N do
     if V[k] = 1 then
       J:= select(`<=`,U +~ k, N);
       V[J]:= V[J] +~ 1;
       U:= [op(U),k];
       F:= ifactors(k)[2]:
       if F[..,2] = [1,1,1,1] then R:= R,k; count:= count+1;  fi;
       break
     fi
   od;
   if k > N then break fi;
od:
R; # Robert Israel, Dec 25 2024

Mathematica

seq[numUlams_] := Module[{ulams = {1, 2}}, Do[AppendTo[ulams, n = Last[ulams]; While[n++; Length[DeleteCases[Intersection[ulams, n - ulams], n/2, 1, 1]] != 2]; n], {numUlams}]; Select[ulams, FactorInteger[#][[;; , 2]] == {1, 1, 1, 1} &]]; seq[1200] (* Amiram Eldar, Dec 24 2024, after Jean-François Alcover at A002858 *)