A074726 Numbers k such that sigma(F(k)) > 2*F(k) where F(k) is the k-th Fibonacci number.

12, 18, 24, 30, 36, 40, 42, 48, 54, 60, 72, 80, 84, 90, 96, 108, 120, 126, 132, 140, 144, 150, 156, 160, 162, 168, 180, 192, 198, 200, 204, 210, 216, 225, 228, 234, 240, 252, 264, 270, 276, 280, 288, 294, 300, 306, 312, 315, 320

Offset

1,1

Comments

Conjecture: sigma(F(n)) > 2*F(n) if and only if F(n) is a Zumkeller number except for n = 12. Verified for n <= 371. - M. Farrokhi D. G., Aug 16 2020

The asymptotic density of this sequence is larger than 184/1225 = 0.1502... (Wall, 1982). - Amiram Eldar, Feb 05 2022

Links

Amiram Eldar, Table of n, a(n) for n = 1..219 (terms 1..156 from T. D. Noe)

Hisanori Mishima, Appendix 1. Factorization results links to internal pages.

Charles R. Wall, Problem H-338, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 20, No. 1 (1982), p. 94; Some Abundance, Solution to Problem H-338 by the proposer, ibid., Vol. 21, No. 2 (1983), pp. 159-160.

Formula

It seems that a(n) is asymptotic to c*n with 6 < c < 6.5.

Mathematica

Select[ Range[256], DivisorSigma[1, Fibonacci[ #1]] > 2*Fibonacci[ #1] & ]

Prog

(PARI) isok(k) = my(f=fibonacci(k)); sigma(f) > 2*f; \\ Michel Marcus, Feb 05 2022

Crossrefs

Cf. A000045, A063477, A074316.

Sequence in context: A341099 A175837 A136446 * A341475 A091013 A348715

Adjacent sequences: A074723 A074724 A074725 * A074727 A074728 A074729

Keyword

nonn

Author

Benoit Cloitre, Sep 04 2002

Extensions

Edited and extended by Robert G. Wilson v, Sep 06 2002

Status

approved