OFFSET
1,2
COMMENTS
Only nonprime numbers are considered because for prime p, p' = 1 = A000045(1).
EXAMPLE
MATHEMATICA
fibQ[n_] := Or @@ IntegerQ /@ Sqrt[5 n^2 + {-4, 4}]; d[0] = d[1] = 0; d[n_] := n*Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); Select[Range[54000], ! PrimeQ[#] && fibQ[d[#]] &] (* Amiram Eldar, May 05 2023 *)
PROG
(Magma) f:=func<n |n le 1 select 0 else n*(&+[Factorisation(n)[i][2] / Factorisation(n)[i][1]: i in [1..#Factorisation(n)]])>; [p:p in [1..54000]|not IsPrime(p) and (IsSquare(5*u*u-4) or IsSquare(5*u*u+4)) where u is Floor(f(p))];
(PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (issquare(k-8)); \\ A000045
isok(k) = !isprime(k) && isfib(ad(k)); \\ Michel Marcus, Jul 05 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Marius A. Burtea, May 03 2023
STATUS
approved