

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



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
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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



