OFFSET
1,2
COMMENTS
Does not contain (for example) 180, so is different from A000028. - Max Alekseyev, Sep 20 2007
How dense is this sequence? There are 7 members up to 10^1, 42 up to 10^2, 364 up to 10^3, 3379 up to 10^4, 31864 up to 10^5, 303623 up to 10^6, 2907125 up to 10^7, 27893864 up to 10^8, and 268099330 up to 10^9. - Charles R Greathouse IV, Sep 16 2015
Partial answer: a(n) << n log n/(log log n)^k for any k. Proof: Since 0 is a Fibonacci number, and Fibonacci numbers are periodic mod any number, 2^(k+1) divides infinitely many Fibonacci numbers. Take some positive Fibonacci number F divisible by 2^(k+1). By Landau's theorem there are >> x (log log x)^k/log x odd squarefree numbers divisible by k+1 primes up to x. Multiply each by 2^(F/2^(k+1)-1) which leaves the density unchanged since the expression is constant in k, and note that the products have exactly F divisors. - Charles R Greathouse IV, Sep 16 2015
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
MATHEMATICA
lim = 250; t = Fibonacci /@ Range@ lim; Select[Range@ lim, MemberQ[t, DivisorSigma[0, #]] &] (* Michael De Vlieger, Sep 16 2015 *)
PROG
(PARI) is(n)=my(k=numdiv(n)^2); issquare(k+=(k+1)<<2)||issquare(k-8) \\ Charles R Greathouse IV, Sep 16 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Giovanni Teofilatto, Oct 04 2006
STATUS
approved