

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.


4



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
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OFFSET

0,2


COMMENTS

The primorial A002110(n) is the smallest squarefree number with n prime factors. Here the nth 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.


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


EXAMPLE

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.


MATHEMATICA

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


CROSSREFS

Cf. A001221, A002110, A005117, A006881, A033992, A287484, A287691.
Sequence in context: A039843 A305937 A286097 * A014853 A131627 A325712
Adjacent sequences: A287480 A287481 A287482 * A287484 A287485 A287486


KEYWORD

nonn,easy,tabf


AUTHOR

Michael De Vlieger, May 25 2017


EXTENSIONS

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


STATUS

approved



