A098833 Numbers n such that the sum of primes dividing n (with repetition) is a Fibonacci number.

1, 2, 3, 5, 6, 13, 15, 16, 18, 22, 38, 56, 63, 68, 75, 80, 89, 90, 93, 96, 106, 108, 145, 174, 195, 208, 231, 233, 234, 253, 275, 289, 330, 343, 352, 396, 490, 494, 588, 644, 664, 695, 700, 705, 747, 752, 834, 836, 840, 846, 884, 896, 916, 920, 945, 959, 1000, 1008

Offset

1,2

Comments

Conjecture: there are infinitely many consecutive terms in this sequence. For example, sopfr(143335) = 377 and sopfr(143336) = 89 are both Fibonacci numbers.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

a(10)=22 because the sum of its prime factors is 13, the 7th
Fibonacci number.

Mathematica

spdfibQ[n_]:=With[{fibs=Fibonacci[Range[30]]}, MemberQ[fibs, Total[ Times@@@ FactorInteger[ n]]]]; Select[Range[1100], spdfibQ] (* Harvey P. Dale, Nov 11 2022 *)

Crossrefs

Cf. A001414.

Sequence in context: A100330 A331043 A020473 * A075371 A218948 A057704

Adjacent sequences: A098830 A098831 A098832 * A098834 A098835 A098836

Keyword

nonn

Author

Jason Earls, Oct 10 2004

Status

approved