A390231 Numbers k such that tau(k) and sigma(k) are both Fibonacci numbers.

1, 2, 7, 9, 66, 70, 23178, 27034, 28678, 28965, 29578, 30094, 32253, 32793, 34113, 35365, 39319, 40963, 8294630, 9124082, 9400558, 9943282, 9943558, 11178399, 12420355, 13550867, 13892383, 14035183, 14068027, 14391187, 14398883, 14642879, 14696207, 2403763482, 3204630082

Offset

1,2

Links

Table of n, a(n) for n=1..35.

Example

k = 66: tau(66) = 8, sigma(66) = 144, both are Fibonacci numbers, thus 66 is a term.

Maple

isfib:= proc(n) issqr(5*n^2+4) or issqr(5*n^2-4) end proc:
select(t -> isfib(NumberTheory:-tau(t)) and isfib(NumberTheory:-sigma(t)), [$1..10^5]);
# Robert Israel, Jan 20 2026

Mathematica

fibQ[k_] := Or @@ IntegerQ /@ Sqrt[5*k^2 + {-4, 4}]; q[k_] := And @@ fibQ /@ DivisorSigma[{0, 1}, k]; Select[Range[42000], q] (* Amiram Eldar, Jan 20 2026 *)

Prog

(PARI) isfib(n) = issquare(5*n^2 - 4) || issquare(5*n^2 + 4);
isok(k) = my(f=factor(k)); isfib(numdiv(f)) && isfib(sigma(f)); \\ Michel Marcus, Jan 20 2026

Crossrefs

Subsequence of A272412.

Cf. A000005, A000045, A000203.

Sequence in context: A041073 A079942 A272412 * A042561 A252661 A362858

Adjacent sequences: A390228 A390229 A390230 * A390232 A390233 A390234

Keyword

nonn

Author

Ctibor O. Zizka, Jan 20 2026

Extensions

More terms from Amiram Eldar, Jan 20 2026

Status

approved