A147956 All positive integers that are not multiples of any Fibonacci numbers >= 2.

1, 7, 11, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 77, 79, 83, 97, 101, 103, 107, 109, 113, 119, 121, 127, 131, 133, 137, 139, 149, 151, 157, 161, 163, 167, 173, 179, 181, 187, 191, 193, 197, 199, 203, 209, 211, 217, 223, 227, 229, 239, 241

Offset

1,2

Comments

This sequence contains a 1 and all terms of sequence A092579 that are not prime Fibonacci numbers.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

77 has the divisors 1,7,11,77. None of these divisors is a Fibonacci number >= 2. So 77 is included in the sequence.

Maple

q:= n-> not ormap(d-> (t-> issqr(t+4) or issqr(t-4)
        )(5*d^2), numtheory[divisors](n) minus {1}):
select(q, [$1..250])[];  # Alois P. Heinz, Jul 15 2022

Mathematica

fibQ[n_] := IntegerQ @ Sqrt[5 n^2 - 4] || IntegerQ @ Sqrt[5 n^2 + 4]; aQ[n_] := !AnyTrue[Rest[Divisors[n]], fibQ]; Select[Range[250], aQ] (* Amiram Eldar, Oct 06 2019 *)

Prog

(PARI) isfib1(n) = if (n>1, my(k=n^2); k+=(k+1)<<2; (issquare(k) || issquare(k-8)));
isok(k) = fordiv(k, d, if (isfib1(d), return(0))); 1; \\ Michel Marcus, Jul 15 2022

Crossrefs

Cf. A092579.

Sequence in context: A349997 A076045 A101618 * A163996 A117743 A216495

Adjacent sequences: A147953 A147954 A147955 * A147957 A147958 A147959

Keyword

nonn

Author

Leroy Quet, Nov 17 2008

Extensions

Extended by Ray Chandler, Nov 24 2008

Status

approved