OFFSET
1,2
COMMENTS
The sequence is infinite as it contains every power of 2 (A000079).
The product of the first five Fermat primes (A019434), 4294967295 = 3 * 5 * 17 * 257 * 65537, is also a member of this sequence.
Every term belongs to A135772.
The first 48 terms are all of the form Sum_{i=1..t} 2^(k*t-1) for some k > 0 and t > 0 (see binary plot in Links section).
LINKS
FORMULA
A295368(a(n)) = a(n).
EXAMPLE
Regarding 170:
- the divisors of 170 are: 1, 2, 5, 10, 17, 34, 85, 170,
- in binary: "1", "10", "101", "1010", "10001", "100010", "1010101", "10101010",
- the corresponding binary plot is:
. 1 . #
. 1 0 . #
. 1 0 1 . # #
. 1 0 1 0 . # #
1 0 0 0 1 # . #
1 0 0 0 1 0 # . #
1 0 1 0 1 0 1 # # # . #
1 0 1 0 1 0 1 0 # # # # .
. .
. .
- this binary plot has reflection symmetry,
- hence 170 belongs to this sequence.
PROG
(PARI) is(n) = { my (d=Vecrev(divisors(n))); if (#binary(d[1])==#d, for (b=0, #d-1, my (t=0); for (i=1, #d, if (bittest(d[i], b), t+=2^(i-1))); if (t!=d[b+1], return (0))); return (1), return (0)) }
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jul 08 2019
STATUS
approved