cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A139588 Nonprime numbers with Fibonacci number of divisors.

Original entry on oeis.org

1, 4, 9, 16, 24, 25, 30, 40, 42, 49, 54, 56, 66, 70, 78, 81, 88, 102, 104, 105, 110, 114, 121, 128, 130, 135, 136, 138, 152, 154, 165, 169, 170, 174, 182, 184, 186, 189, 190, 195, 222, 230, 231, 232, 238, 246, 248, 250, 255, 258, 266, 273, 282, 285, 286, 289
Offset: 1

Views

Author

Omar E. Pol, May 09 2008

Keywords

Comments

A000005(a(n)) is a Fibonacci number.
The union of {1}, A001248, A030514, A030626, A030631, A137484, etc. [From R. J. Mathar, Oct 26 2009]

Links

Crossrefs

Cf. A000005, A000045, A018252, A123193, A139589, A139590.

Programs

  • Mathematica
    Module[{fibs=Fibonacci[Range[20]]},Select[Range[300],!PrimeQ[#]&&MemberQ[ fibs,DivisorSigma[0,#]]&]] (* Harvey P. Dale, Jan 20 2023 *)

Formula

A123193 \ A000040. [From R. J. Mathar, Oct 23 2009]

Extensions

More terms from R. J. Mathar, Oct 23 2009

A139095 Fibonacci numbers whose sum of proper divisors is also a Fibonacci number.

Original entry on oeis.org

1, 1, 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, 99194853094755497, 1066340417491710595814572169, 19134702400093278081449423917, 475420437734698220747368027166749382927701417016557193662268716376935476241
Offset: 1

Views

Author

Omar E. Pol, May 11 2008

Keywords

Comments

Fibonacci numbers k such that A001065(k) is a Fibonacci number.
A001065(a(n)) is a Fibonacci number.
Certainly this contains 1 and the terms of A005478. Does it contain any other terms? - R. J. Mathar, Sep 17 2009
The next term, Fibonacci(359) = 4.754...*10^74, is too large to include in the data section. There are no composite Fibonacci numbers below A000045(1423) in this sequence. - Amiram Eldar, Mar 11 2024

Crossrefs

Cf. A000045, A001065, A005478, A074283, A139589.

Programs

  • Maple
    isA000045 := proc(n) local i,f ; for i from 0 do f := combinat[fibonacci](i) ; if f = n then RETURN(true) ; elif f > n then RETURN(false) ; fi ; od; end: A001065 := proc(n) numtheory[sigma](n)-n ; end: isA139095 := proc(n) RETURN( isA000045(n) and isA000045(A001065(n)) ) ; end: for i from 1 to 230 do if isA139095(combinat[fibonacci](i)) then printf("%d,", combinat[fibonacci](i)) ; fi ; od: # R. J. Mathar, May 22 2008
  • Mathematica
    Fsum[n_]:=DivisorSigma[1,n]-n;Select[Fibonacci[Range[140]],IntegerQ[Sqrt[5*Fsum[#]^2 + 4]] || IntegerQ[Sqrt[5*Fsum[#]^2 - 4]]&] (* James C. McMahon, Jun 28 2025 *)

Extensions

More terms from R. J. Mathar, May 22 2008

A139587 Non-Fibonacci numbers with non-Fibonacci number of divisors.

Original entry on oeis.org

6, 10, 12, 14, 15, 18, 20, 22, 26, 27, 28, 32, 33, 35, 36, 38, 39, 44, 45, 46, 48, 50, 51, 52, 57, 58, 60, 62, 63, 64, 65, 68, 69, 72, 74, 75, 76, 77, 80, 82, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 106, 108, 111
Offset: 1

Views

Author

Omar E. Pol, May 22 2008

Keywords

Comments

A000005(a(n)) is not a Fibonacci number.

Examples

			6 belongs to the sequence because it is not a Fibonacci number and its number of divisors, 4, is also not a Fibonacci number.

Links

Crossrefs

Non-Fibonacci number: A001690. Cf. A000005, A000045, A139095, A139586, A139588, A139589, A139590.

Programs

  • Mathematica
    With[{fibs=Fibonacci[Range[12]]},Select[Range[Max[fibs]],FreeQ[fibs,#] && FreeQ[fibs,DivisorSigma[0,#]]&]] (* Harvey P. Dale, Jun 20 2021 *)

Extensions

Example clarified by Harvey P. Dale, Jun 20 2021

A139586 Non-Fibonacci numbers with Fibonacci number of divisors.

Original entry on oeis.org

4, 7, 9, 11, 16, 17, 19, 23, 24, 25, 29, 30, 31, 37, 40, 41, 42, 43, 47, 49, 53, 54, 56, 59, 61, 66, 67, 70, 71, 73, 78, 79, 81, 83, 88, 97, 101, 102, 103, 104, 105, 107, 109, 110, 113, 114, 121, 127, 128, 130, 131, 135, 136, 137, 138
Offset: 1

Views

Author

Omar E. Pol, May 22 2008

Keywords

Comments

A000005(a(n)) is a Fibonacci number.

Examples

			16 is a term because it is not a Fibonacci number and its number of divisors is 5, a Fibonacci number.

Crossrefs

Non-Fibonacci numbers: A001690.
Cf. A000005, A000045, A139095, A139587, A139588, A139589, A139590.

Programs

  • Mathematica
    fibs=Fibonacci[Range[15]]; nonfibs=Complement[Range[fibs[[-1]]],fibs]; Select[nonfibs,MemberQ[fibs,DivisorSigma[0,#]]&] (* Harvey P. Dale, Jan 11 2011 *)
Showing 1-4 of 4 results.

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