OFFSET
1,2
COMMENTS
Melfi proves that this sequence is infinite. The first few practical Fibonacci numbers have indices that are themselves practical (analogous to the property that the prime Fibonacci numbers have prime indices) but Melfi observes that this property is not true in general: F444 is practical although 444 itself is not.
The indices of these Fibonacci numbers are 1 (and 2), 3, 6, 12, 24, 30, 36, 42, 48, 60, 72, 84, 90, 96, 108, 120, 126, 132, 144, 150, 156, 168, 180, 192, 204, 210, 216, 228, 240, 252, 264, 270, 276, 288, 294, 300, 312, 324, 330, 336, 348, 360, 378, 384, 390, 396, 408, 420, 432, 444, ... - Amiram Eldar, May 29 2017
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..108
Giuseppe Melfi, A survey on practical numbers, Rend. Sem. Mat. Univ. Pol. Torino, 53, (1995), 347-359.
Eric W. Weisstein, From MathWorld: Practical Number.
EXAMPLE
144 is a member of this sequence because it is the 12th Fibonacci number and is also a practical number.
PROG
(PARI) is_A005153(n)=if(n%2, return(n==1)); my(P=1, f=factor(n)); for(i=2, #f~, if(f[i, 1]>1+(P*=sigma(f[i-1, 1]^f[i-1, 2])), return(0))); n>0
print1(1); forstep(n=3, 200, 3, if(is_A005153(t=fibonacci(n)), print1(", "t))) \\ Charles R Greathouse IV, Oct 06 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
David Eppstein, Dec 13 2006
EXTENSIONS
More terms from Charles R Greathouse IV, Oct 06 2013
STATUS
approved