A193292 -id:A193292 - cp's OEIS frontend

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

Jonathan Vos Post, Jul 28 2011

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

			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).

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

Cf. A000032, A001227, A001606, A193292.

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 *)

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

A193293 Sum of odd divisors of Fibonacci(n).

Original entry on oeis.org

1, 1, 1, 4, 6, 1, 14, 32, 18, 72, 90, 13, 234, 420, 372, 1536, 1598, 360, 4332, 12096, 5908, 18000, 28658, 2496, 93062, 122148, 106920, 473760, 514230, 142848, 1349244, 3391488, 1782180, 5708056, 11924808, 1555200, 24664200, 40504200, 31758948, 209212416

Offset: 1

Michel Lagneau, Jul 21 2011

nonn

			a(9) = 18 because Fibonacci(9) = 34 = 2*17 and the sum of the odd divisors
  {1, 17}= 18.

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Cf. A000045, A193292.

Table[Total[Select[Divisors[Fibonacci[n]], OddQ[ # ]&]], {n, 75}]

a(n)=n=fibonacci(n);sigma(n>>valuation(n,2)) \\ Charles R Greathouse IV, Jul 31 2011

a(n) = A000593(A000045(n)). - Michel Marcus, Jan 14 2014

cp's OEIS Frontend

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

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