# Composites Of This Sequence

Leroy Quet q1qq2qqq3qqqq at yahoo.com
Mon Aug 25 00:13:18 CEST 2008

```By the way,
All terms of A037074 are included in the sequence of the composites of A143578.

Are there any other composites?

Thanks,
Leroy Quet

--- On Sun, 8/24/08, Leroy Quet <q1qq2qqq3qqqq at yahoo.com> wrote:

> From: Leroy Quet <q1qq2qqq3qqqq at yahoo.com>
> Subject: Composites Of This Sequence
> To: seqfan at ext.jussieu.fr
> Cc: qq-quet at mindspring.com
> Date: Sunday, August 24, 2008, 9:57 PM
> I just submitted the following (which has yet to appear):
>
> %I A143578
> %S A143578 1,2,3,5,7,11,13,15,17,19,23,29,31,35,37,41,43,47
> %N A143578 A positive integer n is included if (j+n/j)
> divides (k+n/k) for every divisor k of n, where j is the
> largest divisor of n that is <= sqrt(n).
> %C A143578 This sequence trivially contains all the primes.
> %e A143578 The divisors of 35 are 1,5,7,35. The sum of the
> two middle divisors is 5+7 = 12. 12 divides 7 + 35/7 =
> 5+35/5 = 12, of course. And 12 divides 1 + 35/1 = 35 +35/35
> = 36. So 35 is in the sequence.
> %Y A143578 A063655
> %O A143578 1
> %K A143578 ,more,nonn,
>
> What is the sequence of composites of A143578?
>
> It begins: 15, 35,...
>
>
> And, another possible sequence: a(n) = the first term of
> A143578 with 2n divisors.
>
> 2, 15,...
> (1 is the only square in the sequence, since m is coprime
> to m^2 +1.)
>
> Thanks,
> Leroy Quet

```