A124105 - OEIS

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A124105

Practical Fibonacci numbers.

1, 2, 8, 144, 46368, 832040, 14930352, 267914296, 4807526976, 1548008755920, 498454011879264, 160500643816367088, 2880067194370816120, 51680708854858323072, 16641027750620563662096, 5358359254990966640871840 (list; graph; refs; listen; history; text; internal format)

	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 A307326` `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`

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Last modified April 22 07:26 EDT 2021. Contains 343163 sequences. (Running on oeis4.)