# [seqfan] Re: non-multiples of 12 and divisibility of n/p^m, A168186 and A160453

franktaw at netscape.net franktaw at netscape.net
Tue Jan 26 21:42:43 CET 2010

```Correction: for the first question, the number must have at least 3
prime divisors, but not necessarily all distinct.  In fact, 80 is not
in A160453; since the values listed go to 78, and 79 is prime, it is
the first difference.

-----Original Message-----
From: franktaw at netscape.net
To: seqfan at list.seqfan.eu
Sent: Tue, Jan 26, 2010 2:32 pm
Subject: [seqfan] Re: non-multiples of 12 and divisibility of n/p^m,
A168186 and A160453

The answer to the second question is no; 156 is in A023805 but not in
A168186; 121 is in A168186 but not in A023805.

For the first question, the number would have to be a multiple of at
least 3 distinct primes, which should speed up a search.

Shouldn't A160453 say "a prime divisor p" instead of just "a divisor p"?

-----Original Message-----
From: Richard Mathar <mathar at strw.leidenuniv.nl>

Where do these two sequences differ:

http://research.att.com/~njas/sequences/?q=id:A168186|id:A160453
1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22,23,25,26,27,28,29,3

0,31,32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,49,50,51,52,53,54,55,56

,57,58,59,61,62,63,64,65,66,67,68,69,70,71,73,74,75,76,77,78,
1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22,23,25,26,27,28,29,3

0,31,32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,49,50,51,52,53,54,55,56

,57,58,59,61,62,63,64,65,66,67,68,69,70,71,73,74,75,76,77,78

and are these essentially the same:
http://research.att.com/~njas/sequences/?q=id:A168186|id:A023805
1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22,23,25,26,27,28,29,3

0,31,32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,49,50,51,52,53,54,55,56

,57,58,59,61,62,63,64,65,66,67,68,69,70,71,73,74,75,76,77,78,
0,1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22,23,25,26,27,28,29

,30,31,32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,49,50,51,52,53,54,55,

56,57,58,59,61,62,63,64,65,66,67,68,69,70,71,73,74,

```