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%I #41 Jan 28 2019 10:00:55
%S 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,
%T 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,
%U 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
%N Number of divisors of n in OR-numbral arithmetic.
%C See A048888 for the definition of OR-numbral arithmetic. The example shows that this sequence is not multiplicative.
%C In other words, number of lunar divisors of n in base 2.
%H N. J. A. Sloane, <a href="/A067399/b067399.txt">Table of n, a(n) for n = 1..1024</a>
%H D. Applegate, M. LeBrun and N. J. A. Sloane, <a href="http://arxiv.org/abs/1107.1130">Dismal Arithmetic</a> [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
%H D. Applegate, M. LeBrun, N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.html">Dismal Arithmetic</a>, J. Int. Seq. 14 (2011) # 11.9.8.
%H A. Frosini and S. Rinaldi, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL9/Frosini/fros2.html">On the Sequence A079500 and Its Combinatorial Interpretations</a>, J. Integer Seq., Vol. 9 (2006), Article 06.3.1.
%H <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>
%e a(15)=5 since [15] has the 5 OR-numbral divisors [1], [3], [5], [7] and [15].
%e If written as a triangle with rows of lengths 1,2,4,8,16,...:
%e 1,
%e 2, 2,
%e 3, 2, 4, 3,
%e 4, 2, 4, 2, 6, 2, 6, 5,
%e 5, 2, 4, 2, 6, 3, 4, 2, 8, 2, 4, 4, 9, 2, 10, 8,
%e 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,
%e ...,
%e 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
%Y A079500 is the subsequence a(2^k-1). - _N. J. A. Sloane_, Feb 23 2011
%Y Cf. A003986, A007059, A048888, A067138, A067139, A067398, A067400, A067401.
%Y See A188548 for the sum of the divisors.
%K nonn
%O 1,2
%A _Jens Voß_, Jan 23 2002
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