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Relatively Prime Sets and a Phi Function for Subsets of {1, 2, ... , ***n*}

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Min Tang

Department of Mathematics

Anhui Normal University

Wuhu 241000

P. R. China

**Abstract:**

A nonempty subset *A* of {1, 2, ... , *n*} is said to be
relatively prime if gcd(*A*) = 1. Let *f*(*n*) and
*f*_{k}(*n*) denote the number of relatively
prime subsets and the number of relatively prime subsets of cardinality
*k* of {1, 2, ... , *n*}, respectively. Let Φ(*n*)
and Φ_{k}(*n*) denote the number of nonempty
subsets and the number of subsets of cardinality *k* of
{1, 2, ... , *n*} such that gcd(*A*) is relatively prime to *n*,
respectively. In this paper, we obtain some properties of these
functions.

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(Concerned with sequences
A027375
A085945.)

Received March 27 2010;
revised version received July 9 2010.
Published in *Journal of Integer Sequences*, July 16 2010.

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