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

1,2

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

Table of n, a(n) for n=1..52.

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

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

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

Sequence in context: A069588 A088774 A255745 * A290671 A290416 A171230

Adjacent sequences: A188545 A188546 A188547 * A188549 A188550 A188551

Keyword

nonn,base

Author

N. J. A. Sloane, Apr 04 2011

Status

approved