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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

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

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Last modified October 1 04:06 EDT 2020. Contains 337441 sequences. (Running on oeis4.)