A193495 Number of odd divisors of Lucas(n), Lucas numbers beginning at 2.

1, 1, 2, 1, 2, 2, 3, 2, 2, 2, 4, 2, 4, 2, 4, 4, 2, 2, 8, 2, 4, 4, 8, 4, 4, 8, 4, 4, 6, 4, 12, 2, 4, 4, 8, 16, 8, 2, 4, 8, 8, 2, 24, 4, 16, 32, 8, 2, 8, 4, 16, 8, 8, 2, 20, 24, 4, 8, 8, 8, 32, 2, 4, 32, 4, 32, 24, 4, 4, 16, 16, 2, 8, 4, 8, 64, 4, 16, 12, 2, 4

Offset: 0

Author

Jonathan Vos Post, Jul 28 2011

Keywords

• nonn
• easy

Comments

This is to A193292 as A000032 Lucas numbers (beginning at 2) is to A000045 Fibonacci numbers.

Examples

			a(18) = 8 because L(18) = 5778 = 2 * 3^3 * 107 whose odd divisors are 8 in number: {1, 3, 9, 27, 107, 321, 963, 2889}. a(n) = 2 iff n is in A001606 (Indices of prime Lucas numbers).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000032, A001227, A001606, A193292.

Programs

Mathematica

Table[luc = LucasL[n]; r = IntegerExponent[luc, 2]; DivisorSigma[0, luc/2^r], {n, 0, 100}] (* T. D. Noe, Jul 29 2011 *)
Table[Count[Divisors[LucasL[n]],?OddQ],{n,0,80}] (* _Harvey P. Dale, Mar 28 2019 *)

Formula

a(n) = A001227(A000032(n)).