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A333677
Numbers whose divisors can be partitioned into two disjoint sets whose sums are consecutive Fibonacci numbers.
1
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.
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
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Apr 01 2020
EXTENSIONS
a(13)-a(16) from Giovanni Resta, Apr 02 2020
STATUS
approved