A287483 - OEIS

%I #28 Jun 07 2017 19:16:59

%S 1,2,3,5,6,10,14,15,21,22,26,30,42,66,70,78,102,105,110,114,130,138,

%T 154,165,170,174,182,186,190,195,210,330,390,462,510,546,570,690,714,

%U 770,798,858,870,910,930,966,1110,1122,1155,1190,1218,1230,1254,1290

%N 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.

%C 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).

%C A287484(n) gives row lengths.

%H Michael De Vlieger, <a href="/A287483/b287483.txt">Table of n, a(n) for n = 0..10309</a> (rows 0 <= n <= 9).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Primorial.html">Primorial</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Squarefree.html">Squarefree</a>

%e 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.

%e Triangle begins:

%e n   Row n

%e 0:   1;

%e 1:   2,  3,  5;

%e 2:   6, 10, 14, 15, 21,  22,  26;

%e 3:  30, 42, 66, 70, 78, 102, 105, 110, 114, 130, ..., 195;

%e     ...

%e In each row n, the squarefree terms m must have omega(m) = n.

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

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

%K nonn,easy,tabf

%O 0,2

%A _Michael De Vlieger_, May 25 2017

%E Edited by _N. J. A. Sloane_, Jun 05 2017