# [seqfan] Re: Observation on the divisors of 136

WALTER KEHOWSKI wkehowski at cox.net
Sat Dec 30 19:28:21 CET 2017

```Powers of two and 2^(2^n-1)*(2^(2^n)+1) for n=0,1,2,3,4 (the known Fermat primes). Interesting!

>
>     On December 29, 2017 at 5:33 PM Jeremy Gardiner <jeremy.gardiner at btinternet.com> wrote:
>
>     Consider the divisors of 136 (A018299):
>
>     1, 2, 4, 8, 17, 34, 68, 136.
>
>     136 in binary is 10001000.
>
>     Reading off successive bits from the left we have:
>
>     1 1
>     10 2
>     100 4
>     1000 8
>     10001 17
>     100010 34
>     1000100 68
>     10001000 136
>
>     This prompts the question, what other numbers have this property?
>
>     i.e. Numbers whose successive binary shifted parts as decimal numbers are
>     identical to their ordered divisors.
>
>     Clearly, the powers of 2 have this property.
>
>     Also for example 10 in binary is 1010 giving 1, 2, 5, 10.
>
>     The sequence begins:
>
>     1, 2, 3, 4, 8, 10, 16, 32, ... but it is not A295296.
>
>     Regards,
>
>     Jeremy Gardiner
>
>     --
>     Seqfan Mailing list - http://list.seqfan.eu/
>
```