A188288 In lunar arithmetic in base 2, the number of divisors of the number 11...1101 (n digits, the binary expansion of 2^n-3).

0, 1, 0, 2, 2, 2, 4, 6, 10, 16, 31, 55, 100, 185, 345, 644, 1209, 2274, 4298, 8145, 15469, 29454, 56213, 107489, 205925, 395190, 759621, 1462282, 2818799, 5440705, 10513994, 20340794, 39393580, 76368240, 148185145, 287791544, 559386196, 1088144064, 2118283567, 4126561528, 8044217224

Offset: 0

Author

Adam S. Jobson and N. J. A. Sloane, Mar 26 2011

Keywords

• nonn
• base

Comments

a(1)=1 by convention. The g.f. is only a conjecture.

Examples

			a(6) = 4 since 111101 has the divisors 1, 101, 1101, 111101.
a(8) = 10 since 11111101 has the divisors 1, 101, 1001, 1101, 10101, 11001, 11101, 111001, 111101, 11111101.
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..255
• 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]
• Index entries for sequences related to dismal (or lunar) arithmetic

Crossrefs

Cf. A079500, A188524.

Formula

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

Extensions

a(1) in b-file corrected by Andrew Howroyd, Feb 22 2018