A026427 a(n) = least positive integer > a(n-1) and not equal to a(i)*a(j) for 1<=i<=j<=n.

3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 17, 19, 22, 23, 26, 27, 29, 31, 34, 37, 38, 41, 43, 45, 46, 47, 53, 54, 58, 59, 61, 62, 63, 67, 71, 72, 73, 74, 75, 79, 82, 83, 86, 89, 90, 94, 96, 97, 99, 101, 103, 105, 106, 107, 109, 113, 117, 118, 120, 122, 125, 126, 127, 128, 131, 134

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

Starting from 3, include only those numbers that aren't the product of two numbers already included.

Numbers >3 not included: 9,12,15,18,21,24,30,33,39,42,51,57,66,69,78,....

Appears to be A026423 shifted left. - R. J. Mathar, Jun 24 2025

Examples

			9 is excluded because 9=3*3. 10 is included because 10 is not the product of any two of 3,4,5,6,7,8.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A066680.

Cf. A026416 and references therein.

Programs

Mathematica

f[s_List] := Block[{k = s[[ -1]] + 1, ss = Times @@@ Tuples[s, 2]}, While[MemberQ[ss, k], k++ ]; Append[s, k]]; Nest[f, {3}, 65] (* Robert G. Wilson v Sep 23 2006 *)

Extensions

Edited by N. J. A. Sloane, Sep 14 2008 at the suggestion of R. J. Mathar