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# Let $f(n)$ be the sum of the positive integer divisors of $n$. For how many values of $n$, where $1 \le n \le 25$, is $f(n)$ prime?

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Let $f(n)$ be the sum of the positive integer divisors of $n$. For how many values of $n$, where $1 \le n \le 25$, is $f(n)$ prime?

Apr 20, 2018

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+22162
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Let $f(n)$ be the sum of the positive integer divisors of $n$. For how many values of $n$,

where $1 \le n \le 25$, is $f(n)$ prime?

$$\begin{array}{|r|rcr|c|} \hline n & && f(n) & \text{prime} \\ \hline 1 & 1 &=&1 & \\ 2 & 1+2&=&3 & \checkmark \\ 3 & 1+3&=&4 & \\ 4 & 1+2+4&=&7 & \checkmark \\ 5 & 1+5&=&6 & \\ 6 & 1+2+3+6&=&12 & \\ 7 & 1+7&=&8 & \\ 8 & 1+2+4+8&=&15 & \\ 9 & 1+3+9&=&13 & \checkmark \\ 10 & 1+2+5+10&=&18 & \\ 11 & 1+11 &=& 12 & \\ 12 & 1+2+3+4+6+12 &=& 28 & \\ 13 & 1+13 &=& 14 & \\ 14 & 1+2+7+14 &=& 24 & \\ 15 & 1+3+5+15 &=& 24 & \\ 16 & 1+2+4+8+16 &=& 31 & \checkmark \\ 17 & 1+17 &=& 18 & \\ 18 & 1+2+3+6+9+18 &=& 39 & \\ 19 & 1+19 &=& 20 & \\ 20 & 1+2+4+5+10+20 &=& 42 & \\ 21 & 1+3+7+21 &=& 32 & \\ 22 & 1+2+11+22 &=& 36 & \\ 23 & 1+23 &=& 24 & \\ 24 & 1+2+3+4+6+8+12+24 &=& 60 & \\ 25 & 1+5+25 &=& 31 & \checkmark \\ \hline \text{sum } & &&& 5 \\ \hline \end{array}$$

Apr 20, 2018