A063477 -id:A063477 - cp's OEIS frontend

A074283 Sum of the aliquot divisors of n-th Fibonacci number.

0, 0, 1, 1, 1, 7, 1, 11, 20, 17, 1, 259, 1, 43, 506, 549, 1, 2816, 151, 5331, 6778, 289, 1, 110880, 18037, 755, 124342, 155949, 1, 1310680, 2975, 1213179, 1821962, 5169, 2697343, 33280848, 506383, 1416031, 32030858, 106878261, 62159, 295708904, 1

Offset: 1

Shyam Sunder Gupta, Sep 21 2002

nonn

			a(6) = 7 because the sum of the aliquot divisors of the 6th Fibonacci number (i.e. 8) is 1 + 2 + 4 = 7.

Amiram Eldar, Table of n, a(n) for n = 1..1408 (terms 1..250 from Paolo P. Lava)

Cf. A000045, A001065, A063477. - Omar E. Pol, Dec 20 2008

Table[Total[Most[Divisors[n]]],{n,Fibonacci[Range[50]]}] (* Harvey P. Dale, Dec 12 2013 *)

a(n) = A001065(A000045(n)). - Omar E. Pol, Dec 20 2008

a(n) = A063477(n) - A000045(n). - Amiram Eldar, Aug 27 2020

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

Original entry on oeis.org

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

Benoit Cloitre, Sep 04 2002

nonn

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

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.

Cf. A000045, A063477, A074316.

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

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

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

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

A366772 Sum of the divisors of A001045(n) (Jacobsthal numbers).

Original entry on oeis.org

1, 1, 4, 6, 12, 32, 44, 108, 260, 384, 684, 2688, 2732, 5632, 15936, 27864, 43692, 153920, 174764, 499968, 953920, 1477440, 2796204, 11708928, 12253248, 22380544, 69769600, 115568640, 181990200, 620101632, 715827884, 1826150832, 3880589184, 5726797824

Offset: 1

Sean A. Irvine, Oct 21 2023

nonn

			a(9) = 260 because Jacobsthal(9) = 171 has divisors {1, 3, 9, 19, 57, 171}.

Amiram Eldar, Table of n, a(n) for n = 1..1122

Cf. A000203, A001045, A366769, A366770, A366771, A063477.

a(n) = sigma(Jacobsthal(n)) = A000203(A001045(n)).

A366783 Sum of the divisors of A000073(n) (tribonacci numbers).

Original entry on oeis.org

1, 1, 3, 7, 8, 14, 60, 84, 121, 150, 414, 1560, 1352, 2304, 7239, 12480, 10713, 22400, 67032, 154056, 166560, 334880, 770160, 1322090, 2020564, 3712800, 8461404, 21427200, 17008752, 37733696, 154277568, 219104032, 249664896, 341958960, 1575703584, 1997069256

Offset: 2

Sean A. Irvine, Oct 22 2023

nonn

			a(8)=60 because the 8th tribonacci number 24 has divisors {1, 2, 3, 4, 6, 8, 12, 24}.

Amiram Eldar, Table of n, a(n) for n = 2..365

Cf. A000203, A000073, A366780, A366781, A366782, A063477.

DivisorSigma[1, LinearRecurrence[{1, 1, 1}, {1, 1, 2}, 36]] (* Amiram Eldar, Oct 23 2023 *)

a(n) = A000203(A000073(n)).

A350690 Numbers k that divide the sum of divisors of Fibonacci(k).

Original entry on oeis.org

1, 3, 4, 7, 8, 9, 13, 14, 16, 17, 18, 19, 21, 23, 24, 26, 27, 28, 30, 31, 32, 34, 36, 37, 38, 39, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 59, 61, 62, 63, 64, 67, 68, 69, 70, 71, 72, 73, 74, 76, 78, 79, 81, 83, 84, 86, 87, 88, 90, 91, 92, 93, 94, 96

Offset: 1

Amiram Eldar, Jan 12 2022

nonn

This sequence is infinite (Luca, 2002).

			3 is a term since 3 divides sigma(Fibonacci(3)) = sigma(2) = 3.
4 is a term since 4 divides sigma(Fibonacci(4)) = sigma(3) = 4.

Amiram Eldar, Table of n, a(n) for n = 1..1197
Florian Luca, Problem H-590, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 40, No. 5 (2002), p. 472; Arithmetic Functions of Fibonacci Numbers, Solution to Problem H-590 by J.-Ch. Schlage-Puchta and J. Spilker, ibid., Vol. 41, No. 4 (2002), pp. 382-384.

Cf. A000045, A000203, A063477.

Similar sequences: A074698, A075775.

Select[Range[100], Divisible[DivisorSigma[1, Fibonacci[#]], #] &]

from sympy import divisor_sigma, fibonacci
print([k for k in range(1, 97) if divisor_sigma(fibonacci(k)) % k == 0])
# Karl-Heinz Hofmann, Jan 12 2022

A181090 Sum_{d|F(n)} d^3, where F(n) are the Fibonacci numbers.

Original entry on oeis.org

1, 1, 9, 28, 126, 585, 2198, 9632, 44226, 167832, 704970, 3543517, 12649338, 53609220, 257397588, 1000032768, 4073003174, 19720373400, 73088555292, 323884878912, 1476102415284, 5555586582000, 23533806109394

Offset: 1

Michel Lagneau, Oct 02 2010

nonn

			a(6) = 585 is in the sequence because Fibonacci(6) = 8, and 1^3 + 2^3 + 4^3 + 8^3 = 585.

Cf. A000045, A063477, A063478.

Table[Plus@@(Transpose[DivisorSigma[3,Fibonacci[n]]][[1]]), {n, 30}]

A276811 a(n) = sigma(Fibonacci(k))/Fibonacci(n) where k is the least number such that Fibonacci(n) divides sigma(Fibonacci(k)), or -1 if no such k exists.

Original entry on oeis.org

1, 1, 2, 1, 3, 4, 31, 20, 47, 5832, 322, 84, 4576568315415066934826490, 324, 843, 480, 3769607182320, 2209, 707932145558030519866865515025923563263974776037874477588352, 69670959389872974262939756520, 39603

Offset: 1

Altug Alkan, Nov 05 2016

nonn

Least k such that Fibonacci(n) divides sigma(Fibonacci(k)) are 1, 1, 4, 3, 6, 8, 12, 14, 17, 27, 23, 20, 131, 26, 29, 28, 77, 34, 305, 158, 43, ...

			a(7) = 31 because least k such that Fibonacci(7) divides sigma(Fibonacci(k)) is 12 and sigma(Fibonacci(12))/Fibonacci(7) = 31.

Cf. A000045, A063477, A277261.

f[n_] := Block[{k = 1, fn = Fibonacci@ n}, While[ds = DivisorSigma[1, Fibonacci[k]]; Mod[ds, fn] > 0, k++]; ds/fn]; Array[f, 21] (* Robert G. Wilson v, Nov 06 2016 *)

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A074283 Sum of the aliquot divisors of n-th Fibonacci number.

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

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A366772 Sum of the divisors of A001045(n) (Jacobsthal numbers).

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A366783 Sum of the divisors of A000073(n) (tribonacci numbers).

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A350690 Numbers k that divide the sum of divisors of Fibonacci(k).

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A181090 Sum_{d|F(n)} d^3, where F(n) are the Fibonacci numbers.

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A276811 a(n) = sigma(Fibonacci(k))/Fibonacci(n) where k is the least number such that Fibonacci(n) divides sigma(Fibonacci(k)), or -1 if no such k exists.

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