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

%I A379532 #13 Jan 03 2025 14:55:08
%S A379532 390,546,690,798,1155,1230,1770,2010,2090,2418,2618,2814,3090,3290,
%T A379532 3390,3930,4326,4370,4470,4578,4602,4641,6110,6870,7170,7490,7735,
%U A379532 7930,8294,9834,10110,10545,10738,11102,11346,11390,11454,11622,11715,11886,12270,12441,12470,12570
%N A379532 Ulam numbers that are products of exactly four distinct primes (or tetraprimes).
%C A379532 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.
%H A379532 Robert Israel, <a href="/A379532/b379532.txt">Table of n, a(n) for n = 1..6826</a>
%e A379532 390 is a term because 390=2*3*5*13 is the product of 4 distinct primes and 390 is an Ulam number.
%e A379532 546 is a term because 546=2*3*7*13 is the product of 4 distinct primes and 546 is an Ulam number.
%e A379532 1155 is a term because 1155=3*5*7*11 is the product of 4 distinct primes and 1155 is an Ulam number.
%p A379532 N:= 20000: # for terms <= N
%p A379532 U:= [1,2]: V:= Vector(N): V[3]:= 1: R:= NULL: count:= 0:
%p A379532 for i from 3 do
%p A379532    for k from U[-1]+1 to N do
%p A379532      if V[k] = 1 then
%p A379532        J:= select(`<=`,U +~ k, N);
%p A379532        V[J]:= V[J] +~ 1;
%p A379532        U:= [op(U),k];
%p A379532        F:= ifactors(k)[2]:
%p A379532        if F[..,2] = [1,1,1,1] then R:= R,k; count:= count+1;  fi;
%p A379532        break
%p A379532      fi
%p A379532    od;
%p A379532    if k > N then break fi;
%p A379532 od:
%p A379532 R; # _Robert Israel_, Dec 25 2024
%t A379532 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 *)
%Y A379532 Intersection of A002858 and A046386.
%Y A379532 Cf. A068820, A378795, A379162.
%K A379532 nonn
%O A379532 1,1
%A A379532 _Massimo Kofler_, Dec 24 2024