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 A067399 Number of divisors of n in OR-numbral arithmetic. 10
 1, 2, 2, 3, 2, 4, 3, 4, 2, 4, 2, 6, 2, 6, 5, 5, 2, 4, 2, 6, 3, 4, 2, 8, 2, 4, 4, 9, 2, 10, 8, 6, 2, 4, 2, 6, 2, 4, 2, 8, 2, 6, 2, 6, 4, 4, 4, 10, 2, 4, 4, 6, 2, 8, 4, 12, 2, 4, 4, 15, 4, 16, 14, 7, 2, 4, 2, 6, 2, 4, 2, 8, 3, 4, 2, 6, 2, 4, 2, 10, 2, 4, 2, 9, 5, 4, 2, 8, 2, 8, 4, 6, 2, 8, 6, 12, 2, 4, 4, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A048888 for the definition of OR-numbral arithmetic. The example shows that this sequence is not multiplicative. In other words, number of lunar divisors of n in base 2. LINKS N. J. A. Sloane, Table of n, a(n) for n = 1..1024 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] D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8. A. Frosini and S. Rinaldi, On the Sequence A079500 and Its Combinatorial Interpretations, J. Integer Seq., Vol. 9 (2006), Article 06.3.1. EXAMPLE a(15)=5 since [15] has the 5 OR-numbral divisors [1], [3], [5], [7] and [15]. If written as a triangle with rows of lengths 1,2,4,8,16,...: 1, 2, 2, 3, 2, 4, 3, 4, 2, 4, 2, 6, 2, 6, 5, 5, 2, 4, 2, 6, 3, 4, 2, 8, 2, 4, 4, 9, 2, 10, 8, 6, 2, 4, 2, 6, 2, 4, 2, 8, 2, 6, 2, 6, 4, 4, 4, 10, 2, 4, 4, 6, 2, 8, 4, 12, 2, 4, 4, 15, 4, 16, 14, ..., the last terms in each row give A079500(n). The penultimate terms in the rows give 2*A079500(n-1). - N. J. A. Sloane, Mar 05 2011 CROSSREFS A079500 is the subsequence a(2^k-1). - N. J. A. Sloane, Feb 23 2011 Cf. A003986, A007059, A048888, A067138, A067139, A067398, A067400, A067401. See A188548 for the sum of the divisors. Sequence in context: A334857 A331614 A060025 * A106737 A323164 A318881 Adjacent sequences:  A067396 A067397 A067398 * A067400 A067401 A067402 KEYWORD nonn AUTHOR Jens Voß, Jan 23 2002 STATUS approved

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Last modified May 31 19:40 EDT 2020. Contains 334748 sequences. (Running on oeis4.)