[seqfan] Re: Observation on the divisors of 136

[WALTER KEHOWSKI]

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
> 
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