A160683 Numbers n >= 1 such that A000045(n)/A000005(A000045(n)) is an integer.

1, 2, 3, 6, 24, 48

Offset: 1

Author

Ctibor O. Zizka, May 23 2009

Keywords

• nonn
• fini
• full

Comments

No further term between 48 and 320. - R. J. Mathar, Apr 01 2011

This sequence is complete. For proof see the Luca-Young paper in links section, pages 7-10. - Altug Alkan, Apr 26 2016

Links

• Florian Luca and Paul Thomas Young, On the number of divisors of n! and of the Fibonacci numbers, Glasnik Matematicki, Vol. 47, No. 2 (2012), 285-293. DOI: 10.3336/gm.47.2.05.

Crossrefs

Cf. A000005, A000045, A063375, A160686.

Programs

Maple

with(combinat):with(numtheory): A160683 := proc(n) option remember: local k: if(n=1)then return 1:fi: for k from procname(n-1)+1 do if(fibonacci(k) mod tau(fibonacci(k))=0)then return k:fi: od: end: seq(A160683(n), n=1..6); # Nathaniel Johnston, May 09 2011

Mathematica

Select[Range@ 120, IntegerQ[#/DivisorSigma[0, #]] &@ Fibonacci@ # &]

PARI

isok(n) = my(f=fibonacci(n)); f % numdiv(f) == 0; \\ Michel Marcus, Jul 31 2015

Formula

{n: A063375(n) | A000045(n)} . - R. J. Mathar, Apr 01 2011