A333677 Numbers whose divisors can be partitioned into two disjoint sets whose sums are consecutive Fibonacci numbers.

1, 2, 66, 70, 18084, 19180, 24934, 26715, 5346390, 8197798, 8424178, 9088863, 1874967204, 1988601580, 2585182054, 2769837915

Offset

1,2

Comments

Since the sum of divisors of each term is also a Fibonacci number, this sequence is a subsequence of A272412.

Links

Table of n, a(n) for n=1..16.

Formula

66 is a term since its divisors {1, 2, 3, 6, 11, 22, 33, 66} can be partitioned into the two disjoint sets, {2, 3, 6, 11, 33} and {1, 22, 66}, whose sums, 55 and 89, are 2 consecutive Fibonacci numbers.

Mathematica

fibs = Fibonacci @ Range[2, 40]; seqQ[n_] := MemberQ[fibs, DivisorSigma[1, n]] && Module[{d = Divisors[n], s}, s = Round[Plus @@ d/GoldenRatio]; c = CoefficientList[Product[1 + x^i, {i, d}], x]; c[[1 + s]] > 0]; Select[Range[10^5], seqQ]

Crossrefs

Cf. A000045, A000203, A083207, A272412.

Sequence in context: A265996 A309169 A231946 * A098089 A304934 A075809

Adjacent sequences: A333674 A333675 A333676 * A333678 A333679 A333680

Keyword

nonn,more

Author

Amiram Eldar, Apr 01 2020

Extensions

a(13)-a(16) from Giovanni Resta, Apr 02 2020

Status

approved