A115105 Numbers of the form p^F(i)*q^F(j), where p and q are distinct primes; F(i) and F(j) are Fibonacci numbers.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 79, 82, 83

Offset: 1

Author

Giovanni Teofilatto, Mar 03 2006; corrected Mar 04 2006

Keywords

• nonn

Comments

All the primes are in the sequence, since they are of the form p^F(0)*q^F(1) with p^F(0) = p^0 = 1.

Examples

			a(1) = 1 because 2^0*3^0 = 1;
a(3) = 3 because 3^1*5^0 = 3;
a(4) = 4 because 2^2*3^0 = 4;
a(6) = 6 because 2^1*3^1 = 6.
		

Links

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

Crossrefs

Cf. A115063.

Programs

Mathematica

fibQ[n_] := IntegerQ @ Sqrt[5 n^2 - 4] || IntegerQ @ Sqrt[5 n^2 + 4]; aQ[n_] :=Length[ (e=FactorInteger[n][[;;, 2]])]<3 && AllTrue[e, fibQ]; Select[Range[100], aQ] (* Amiram Eldar, Oct 06 2019 *)

Extensions

2 missing terms inserted by Amiram Eldar, Oct 06 2019