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%I #42 Feb 22 2018 17:33:17
%S 0,1,0,2,2,2,4,6,10,16,31,55,100,185,345,644,1209,2274,4298,8145,
%T 15469,29454,56213,107489,205925,395190,759621,1462282,2818799,
%U 5440705,10513994,20340794,39393580,76368240,148185145,287791544,559386196,1088144064,2118283567,4126561528,8044217224
%N In lunar arithmetic in base 2, the number of divisors of the number 11...1101 (n digits, the binary expansion of 2^n-3).
%C a(1)=1 by convention. The g.f. is only a conjecture.
%H N. J. A. Sloane, <a href="/A188288/b188288.txt">Table of n, a(n) for n = 0..255</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 <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>
%F G.f.: x + x^3/(1-x) + Sum(x^l*(1-x)^2/(1-2*x+x^(l-1)-x^l+x^(l+2)), l=3..oo). - _N. J. A. Sloane_, Apr 19 2011
%e a(6) = 4 since 111101 has the divisors 1, 101, 1101, 111101.
%e a(8) = 10 since 11111101 has the divisors 1, 101, 1001, 1101, 10101, 11001, 11101, 111001, 111101, 11111101.
%Y Cf. A079500, A188524.
%K nonn,base
%O 0,4
%A _Adam S. Jobson_ and _N. J. A. Sloane_, Mar 26 2011
%E a(1) in b-file corrected by _Andrew Howroyd_, Feb 22 2018