A188548 The sum of the divisors of n in base-2 lunar arithmetic.

1, 11, 11, 111, 101, 111, 111, 1111, 1001, 1111, 1011, 1111, 1101, 1111, 1111, 11111, 10001, 11011, 10011, 11111, 10101, 11111, 10111, 11111, 11001, 11111, 11011, 11111, 11101, 11111, 11111, 111111, 100001, 110011, 100011, 111111, 100101, 110111, 100111, 111111, 101001, 111111, 101011, 111111, 101101, 111111, 101111, 111111, 110001, 111011, 110011, 111111

Offset: 1

Author

N. J. A. Sloane, Apr 04 2011

Keywords

• nonn
• base

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.

Examples

			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).
		

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]
• N. J. A. Sloane, Table giving n (written in base 10), n (written in base 2), a(n) (written in base 2), a(n) (written in base 10)
• Index entries for sequences related to dismal (or lunar) arithmetic

Crossrefs

Cf. A067399 (number of divisors), A190149, A190632.