# [seqfan] Re: Pairs Occurring Only Once Among # Of Divisors

T. D. Noe noe at sspectra.com
Fri Jun 26 19:33:55 CEST 2009

```>[1, 2, 3, 4, 8, 15, 16, 24, 35, 48, 63, 64, 80, 99, 288, 528, 575, 624,
>728, 960, 1023, 1024, 1088, 1295, 2303, 2400, 4095, 4096, 5328, 6399,
>6723, 9408, 9999, 14640, 15624, 28223, 36863, 38415, 46655, 50175,
>50624, 57121, 59048, 59049, 65535, 65536, 71824, 82944, 83520, 117648,
>130320, 146688, 250000, 262143, 262144, 263168, 279840, 331775, 421200,
>529983, 531440, 531441, 589824, 640000, 641600, 651249, 746495, 746496,
>777924, 860624, 861183, 923520, 937024, 1000000]
>
>Some of these aren't in the sequence, they just didn't hit a match
>before 10^8.  For instance, 1000000 is matched by 94^6, which didn't
>take long to find.

71824 isn't in the sequence because it is matched by  868834576
82944 isn't in the sequence because it is matched by 1686498489

A while ago someone wrote

>Thus A161460 contains at least all Mersenne primes

This is false for Mersenne primes > 3:
7 is matched by 5
31 is matched by 11
127 is matched by 23
8191 is matched by 191
131071 is matched by 179
524287 is matched by 139

I can prove 288 is in the sequence.

It appears that p^(q-1)-1 is in the sequence for many primes p and q.
For p=2, we have terms for q=3,5,7,11,13,17
For p=3, we have terms for q=3,5,7,11,13
For p=5, we have terms for q=3,5,7
For p=7, we have terms for q=3,5,7
For p=11, we have terms for q=5

Tony

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