[seqfan] Observation on the divisors of 136

[Jeremy Gardiner]

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