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

1,2

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.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A115063.

Sequence in context: A046100 A337138 A023757 * A121176 A028261 A119675

Adjacent sequences: A115102 A115103 A115104 * A115106 A115107 A115108

Keyword

nonn

Author

Giovanni Teofilatto, Mar 03 2006; corrected Mar 04 2006

Extensions

2 missing terms inserted by Amiram Eldar, Oct 06 2019

Status

approved