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A174279 Smallest k such that tau(Fibonacci(k)) = 2^n. 0
1, 3, 6, 15, 18, 44, 30, 54, 128, 80, 138, 90, 162, 198, 308, 294, 210, 460, 288, 270, 378, 510, 680, 594, 920, 570, 690 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Smallest k such that A000005(A000045(k)) = 2^n.

The multiplicative property of the tau-function implies that the Fibonacci(k) has a prime factor representation p_1^e_1*p_2^e_2*.. where (e_1+1)*(e_2+1)*.. is a power of 2, that is, the exponents are in {1,3,7,15,...}. This adds for example the squarefree Fibonacci numbers with indices from A037918 to the list of candidates. - R. J. Mathar, Oct 11 2011

REFERENCES

Mohammad K. Azarian, The Generating Function for the Fibonacci Sequence, Missouri Journal of Mathematical Sciences, Vol. 2, No. 2, Spring 1990, pp. 78-79. Zentralblatt MATH, Zbl 1097.11516.

Majorie Bicknell and Verner E Hoggatt, Fibonacci's Problem Book, Fibonacci Association, San Jose, Calif., 1974.

LINKS

Table of n, a(n) for n=0..26.

N. D. Cahill and D. A. Narayan, Fibonacci and Lucas Numbers as Tridiagonal Matrix Determinants, Fibonacci Quarterly, 42(3):216-221, 2004.

S. Happersett, Mathematical meditations , J. Math. Arts 1 (1) (2007) 29-33.

EXAMPLE

a(0) = 1 because tau(Fibonacci(1))=tau(1)= 2^0 = 1.

a(1) = 3 because tau(Fibonacci(3))=tau(2)= 2^1=2.

a(2) = 6 because tau(Fibonacci(6))=tau(8)= 2^2= 4.

a(3) = 15 because tau(Fibonacci(15))= tau(610)=2^3=8.

MAPLE

with(numtheory):for p from 1 to 100 do:indic:=0:u0:=0:u1:=1:for n from 2 to 1000 while(indic=0)do:s:=u0+u1:u0:=u1:u1:=s:if tau(s)= 2^p and indic=0 then print(p): print(n): indic:=1:else fi:od:od:

CROSSREFS

Cf. A085077, A063375.

Sequence in context: A212060 A249246 A248969 * A233554 A276546 A265486

Adjacent sequences:  A174276 A174277 A174278 * A174280 A174281 A174282

KEYWORD

nonn,more

AUTHOR

Michel Lagneau, Mar 15 2010

STATUS

approved

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Last modified January 16 15:31 EST 2019. Contains 319195 sequences. (Running on oeis4.)