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A188548
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The sum of the divisors of n in base 2 lunar arithmetic.
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7
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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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
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EXAMPLE
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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).
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CROSSREFS
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Cf. A067399 (number of divisors), A190149, A190632.
Sequence in context: A069588 A088774 A255745 * A290671 A290416 A171230
Adjacent sequences: A188545 A188546 A188547 * A188549 A188550 A188551
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KEYWORD
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nonn,base
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AUTHOR
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N. J. A. Sloane, Apr 04 2011
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STATUS
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approved
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