A119433 - OEIS

%I #14 Nov 07 2020 11:36:42

%S 2,105,165,195,3003,3927,4389,4641,4845,5187,5313,5865,6555,7395,7905,

%T 8265,8835,9435,10005,10455,10545,10695,10965,11685,11985,12255,12765,

%U 13395,13485,13515,14145,14835,15045,15105,15555,16215,16815,17085

%N Primitive elements of A119432.

%C Elements of A119432 that are not divisible by any smaller element of that sequence.

%C Appears to be the lexicographically latest sequence of squarefree numbers such that all numbers with abundance >= -1 (see A103288) are divisible by one of the terms. - _Peter Munn_, Oct 19 2020

%H Charles R Greathouse IV, <a href="/A119433/b119433.txt">Table of n, a(n) for n = 1..10000</a>

%F 2 followed by odd elements of A119431.

%e From _Peter Munn_, Oct 23 2020: (Start)

%e Initial terms, showing factorization:

%e    n   a(n)

%e    1      2 = 2

%e    2    105 = 3 * 5 * 7

%e    3    165 = 3 * 5 * 11

%e    4    195 = 3 * 5 * 13

%e    5   3003 = 3 * 7 * 11 * 13

%e    6   3927 = 3 * 7 * 11 * 17

%e    7   4389 = 3 * 7 * 11 * 19

%e    8   4641 = 3 * 7 * 13 * 17

%e    9   4845 = 3 * 5 * 17 * 19

%e   10   5187 = 3 * 7 * 13 * 19

%e   11   5313 = 3 * 7 * 11 * 23

%e   12   5865 = 3 * 5 * 17 * 23

%e   13   6555 = 3 * 5 * 19 * 23

%e   14   7395 = 3 * 5 * 17 * 29

%e   15   7905 = 3 * 5 * 17 * 31

%e (End)

%t Block[{a = {}}, Do[If[And[NoneTrue[a, Mod[i, #] == 0 &], 2 EulerPhi[i] <= i], AppendTo[a, i]], {i, 20000}]; a] (* _Michael De Vlieger_, Nov 05 2020 *)

%Y Subsequence of A005117, A119432.

%Y Cf. A103288.

%K nonn

%O 1,1

%A _Franklin T. Adams-Watters_, May 19 2006