OFFSET
1,2
COMMENTS
More precisely, in base-2 lunar arithmetic, the lunar sum of the lunar divisors of the n-th nonzero binary number.
Theorem: a(n) = binary representation of n iff n is odd.
LINKS
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
EXAMPLE
The 4th binary number is 100 which has lunar divisors 1, 10, 100, whose lunar sum is 111, so a(4)=111.
The 5th binary number is 101 which has lunar divisors 1 and 101, whose lunar sum is 101, so a(5)=101.
It might be tempting to conjecture that if n is even then a(n) = 111...111, but a(18)=11011 shows that this is false (see A190149).
CROSSREFS
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Apr 04 2011
STATUS
approved