Strung out on necklaces ... :-/

[Jon Schoenfield]

All,

My apologies in advance if this is a dumb question (or a set of n dumb questions where n > 1) ...

I'm having trouble understanding the definition of sequence A062163.  If anyone's interested and has time, could someone tell me

(1) what "reduces exactly" means (in the Extension field for A062163) in the sentence, "The sequence reduces exactly the objects of A000029"?

(2) whether the sense in which the word "similar" is used (in "similar necklaces count only once") is fairly common in mathematics?  It seems counterintuitive to me.

Thanks for your time,

-- Jon
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