A381189 Ulam numbers that are squarefree semiprimes.

6, 26, 38, 57, 62, 69, 77, 82, 87, 106, 145, 155, 177, 206, 209, 219, 221, 253, 309, 319, 339, 341, 358, 382, 451, 485, 497, 502, 566, 685, 695, 734, 781, 849, 866, 893, 905, 949, 1018, 1037, 1079, 1081, 1101, 1157, 1167, 1169, 1186, 1191, 1257, 1313, 1355, 1387, 1389

Offset: 1

Author

Massimo Kofler, Feb 16 2025

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.

Number such as 4, 2809, 3481, 6889, etc., are in A378795 but not in this or in a longer sequence.

Examples

			4 is not a term of this sequence because 4=2^2 is the product of 2 not distinct primes even if 4 is an Ulam number.
6 is a term because 6=2*3 is the product of 2 distinct primes and 6 is an Ulam number.
57 is a term because 57=3*19 is the product of 2 distinct primes and 57 is an Ulam number.
2809 is not a term of a longer sequence because 2809=53^2 is the product of 2 not distinct primes even if 2809 is an Ulam number.
		

Crossrefs

Intersection of A006881 and A002858.

Cf. A068820, A378795, A379162, A379532.

Programs

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} &]]; seq[160] (* Amiram Eldar, Feb 16 2025, after Jean-François Alcover at A002858 *)