A390231 - OEIS

%I #23 Jan 24 2026 15:44:43

%S 1,2,7,9,66,70,23178,27034,28678,28965,29578,30094,32253,32793,34113,

%T 35365,39319,40963,8294630,9124082,9400558,9943282,9943558,11178399,

%U 12420355,13550867,13892383,14035183,14068027,14391187,14398883,14642879,14696207,2403763482,3204630082

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

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

%p isfib:= proc(n) issqr(5*n^2+4) or issqr(5*n^2-4) end proc:

%p select(t -> isfib(NumberTheory:-tau(t)) and isfib(NumberTheory:-sigma(t)), [$1..10^5]);

%p # _Robert Israel_, Jan 20 2026

%t 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 *)

%o (PARI) isfib(n) = issquare(5*n^2 - 4) || issquare(5*n^2 + 4);

%o isok(k) = my(f=factor(k)); isfib(numdiv(f)) && isfib(sigma(f)); \\ _Michel Marcus_, Jan 20 2026

%Y Subsequence of A272412.

%Y Cf. A000005, A000045, A000203.

%K nonn

%O 1,2

%A _Ctibor O. Zizka_, Jan 20 2026

%E More terms from _Amiram Eldar_, Jan 20 2026