

A193495


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


3



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
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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 A240872 A328806
Adjacent sequences: A193492 A193493 A193494 * A193496 A193497 A193498


KEYWORD

nonn,easy


AUTHOR

Jonathan Vos Post, Jul 28 2011


STATUS

approved



