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

Author

Amiram Eldar, Apr 01 2020

Keywords

• nonn
• more

Comments

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

Crossrefs

Cf. A000045, A000203, A083207, A272412.

Programs

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]

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.

Extensions

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