cp's OEIS Frontend

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

%I A147956 #17 Jul 15 2022 13:53:00
%S A147956 1,7,11,17,19,23,29,31,37,41,43,47,49,53,59,61,67,71,73,77,79,83,97,
%T A147956 101,103,107,109,113,119,121,127,131,133,137,139,149,151,157,161,163,
%U A147956 167,173,179,181,187,191,193,197,199,203,209,211,217,223,227,229,239,241
%N A147956 All positive integers that are not multiples of any Fibonacci numbers >= 2.
%C A147956 This sequence contains a 1 and all terms of sequence A092579 that are not prime Fibonacci numbers.
%H A147956 Amiram Eldar, <a href="/A147956/b147956.txt">Table of n, a(n) for n = 1..10000</a>
%e A147956 77 has the divisors 1,7,11,77. None of these divisors is a Fibonacci number >= 2. So 77 is included in the sequence.
%p A147956 q:= n-> not ormap(d-> (t-> issqr(t+4) or issqr(t-4)
%p A147956         )(5*d^2), numtheory[divisors](n) minus {1}):
%p A147956 select(q, [$1..250])[];  # _Alois P. Heinz_, Jul 15 2022
%t A147956 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 *)
%o A147956 (PARI) isfib1(n) = if (n>1, my(k=n^2); k+=(k+1)<<2; (issquare(k) || issquare(k-8)));
%o A147956 isok(k) = fordiv(k, d, if (isfib1(d), return(0))); 1; \\ _Michel Marcus_, Jul 15 2022
%Y A147956 Cf. A092579.
%K A147956 nonn
%O A147956 1,2
%A A147956 _Leroy Quet_, Nov 17 2008
%E A147956 Extended by _Ray Chandler_, Nov 24 2008