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 A188548 The sum of the divisors of n in base 2 lunar arithmetic. 7
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified April 12 11:51 EDT 2021. Contains 342920 sequences. (Running on oeis4.)