A287483 Irregular triangle T(n,k) read by rows: row n lists numbers m with A002110(n) <= m < A002110(n+1) such that omega(m) = n.

1, 2, 3, 5, 6, 10, 14, 15, 21, 22, 26, 30, 42, 66, 70, 78, 102, 105, 110, 114, 130, 138, 154, 165, 170, 174, 182, 186, 190, 195, 210, 330, 390, 462, 510, 546, 570, 690, 714, 770, 798, 858, 870, 910, 930, 966, 1110, 1122, 1155, 1190, 1218, 1230, 1254, 1290

Offset: 0

Author

Michael De Vlieger, May 25 2017

Keywords

• nonn
• easy
• tabf

Comments

The primorial A002110(n) is the smallest squarefree number with n prime factors. Here the n-th row of the triangle is a list of squarefree numbers with n prime factors greater than and including A002110(n) but less than A002110(n+1).

A287484(n) gives row lengths.

Examples

			The sequence begins with 1 as it is equal to A002110(0) and has 0 prime factors. The first primes less than 6 come next, followed by the first squarefree semiprimes (A006881) less than 30 and the smallest terms of A033992 less than 210, etc.
Triangle begins:
n   Row n
0:   1;
1:   2,  3,  5;
2:   6, 10, 14, 15, 21,  22,  26;
3:  30, 42, 66, 70, 78, 102, 105, 110, 114, 130, ..., 195;
    ...
In each row n, the squarefree terms m must have omega(m) = n.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10309 (rows 0 <= n <= 9).
• Eric Weisstein's World of Mathematics, Primorial
• Eric Weisstein's World of Mathematics, Squarefree

Crossrefs

Cf. A001221, A002110, A005117, A006881, A033992, A287484, A287691.

Programs

Mathematica

Table[Select[Range[#, Prime[n + 1] # - 1] &@ Product[Prime@ i, {i, n}], And[SquareFreeQ@ #, PrimeOmega@ # == n] &], {n, 0, 4}] // Flatten

Extensions

Edited by N. J. A. Sloane, Jun 05 2017