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

Author

Benoit Cloitre, Sep 04 2002

Keywords

• nonn

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.

Crossrefs

Cf. A000045, A063477, A074316.

Programs

Mathematica

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

PARI

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

Formula

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

Extensions

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