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

0,3

Comments

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

Links

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

Formula

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

Example

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).

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 *)

Crossrefs

Cf. A000032, A001227, A001606, A193292.

Sequence in context: A057526 A033265 A096004 * A071068 A352104 A240872

Adjacent sequences: A193492 A193493 A193494 * A193496 A193497 A193498

Keyword

nonn,easy

Author

Jonathan Vos Post, Jul 28 2011

Status

approved