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==Idea==
 
==Idea==
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Let <math>\text{p}_i\!</math> be the <math>i^\text{th}\!</math> prime, taking <math>2\!</math> as the <math>1^\text{st}\!</math> prime in the sequence that begins as follows:
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Let <math>\text{p}_i</math> be the <math>i^\text{th}</math> prime, where <math>i</math> is a positive integer called the ''index'' of the prime  <math>\text{p}_i</math> and the indices are taken such that <math>\text{p}_1 = 2.</math> Thus the sequence <math>\text{p}_i</math> begins as follows:
    
{| align="center" cellpadding="6" width="90%"
 
{| align="center" cellpadding="6" width="90%"
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\end{matrix}</math>
 
\end{matrix}</math>
 
|}
 
|}
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The positive integer <math>i</math> is the ''index'' of the prime <math>\text{p}_i.</math>
      
Let <math>I(n)</math> be the set of indices of primes that divide the positive integer <math>n.</math>
 
Let <math>I(n)</math> be the set of indices of primes that divide the positive integer <math>n.</math>
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