

A109054


Numbers n such that the continued fraction expansion of sqrt(n) is multiplicative.


1



0, 1, 3, 4, 7, 8, 9, 13, 14, 15, 16, 22, 23, 24, 25, 32, 33, 34, 35, 36, 44, 47, 48, 49, 58, 59, 60, 62, 63, 64, 74, 75, 78, 79, 80, 81, 95, 96, 98, 99, 100, 114, 119, 120, 121, 135, 136, 138, 140, 141, 142, 143, 144, 160, 162, 164, 167, 168, 169, 185, 187, 189, 192
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OFFSET

1,3


COMMENTS

Perfect squares are assumed to have a continued fraction expansion of all zeros after a(0) and so are trivially multiplicative
For nonsquares, a(1) must be 1 and so n must satisfy k+1/2 < sqrt(n) <= k+1, for some integer k.


LINKS

Table of n, a(n) for n=1..63.


EXAMPLE

The continued fraction of sqrt(22) is (4; 1, 2, 4, 2, 1, 8, ...), which is multiplicative with a(2^e) = 2, a(3^e) = 4, a(p^e) = 1 otherwise.


CROSSREFS

Cf. A040001, A010121, A040005, etc.
Sequence in context: A226227 A100452 A004201 * A129142 A075752 A046541
Adjacent sequences: A109051 A109052 A109053 * A109055 A109056 A109057


KEYWORD

nonn,easy


AUTHOR

Mitch Harris, Jun 18 2005


STATUS

approved



