A120499 Irregular triangle read by rows in which the n-th row consists of the positive integers which are <= n and divisible by exactly one prime dividing n (but are coprime to every other prime dividing n). (a(1) = 1).

1, 2, 3, 2, 4, 5, 2, 3, 4, 7, 2, 4, 6, 8, 3, 6, 9, 2, 4, 5, 6, 8, 11, 2, 3, 4, 8, 9, 10, 13, 2, 4, 6, 7, 8, 10, 12, 3, 5, 6, 9, 10, 12, 2, 4, 6, 8, 10, 12, 14, 16, 17, 2, 3, 4, 8, 9, 10, 14, 15, 16, 19, 2, 4, 5, 6, 8, 12, 14, 15, 16, 18, 3, 6, 7, 9, 12, 14, 15, 18, 2, 4, 6, 8, 10, 11, 12, 14, 16, 18

Offset: 1

Author

Leroy Quet, Aug 06 2006

Keywords

• nonn
• tabf

Comments

n-th row of array has A116512(n) terms.

Examples

			12 is divisible by the primes 2 and 3. 2,3,4,8,9,10 are those positive integers which are <= 12, which are divisible by 2 or 3, but are not divisible by 2 and 3. So the 12th row of the array is {2,3,4,8,9,10}.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10589 (rows 1 <= n <= 250)

Crossrefs

Cf. A116512, A119790, A119794.

Programs

Mathematica

Table[Select[Range@ n, Function[k, Total@ Boole@ Map[Divisible[k, #] &, FactorInteger[n][[All, 1]]] == 1]], {n, 22}] // Flatten (* Michael De Vlieger, Sep 30 2017 *)

Extensions

Corrected by Ray Chandler, Aug 29 2006