A124105 Practical Fibonacci numbers.

1, 2, 8, 144, 46368, 832040, 14930352, 267914296, 4807526976, 1548008755920, 498454011879264, 160500643816367088, 2880067194370816120, 51680708854858323072, 16641027750620563662096, 5358359254990966640871840

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

Cf. A000045, A005153, A074316.

Sequence in context: A154908 A166356 A009817 * A079613 A091299 A362729

Adjacent sequences: A124102 A124103 A124104 * A124106 A124107 A124108

Keyword

nonn

Author

David Eppstein, Dec 13 2006

Extensions

More terms from Charles R Greathouse IV, Oct 06 2013

Status

approved