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seen Feb 14 '13 at 15:19

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asked Question about set notation
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Feb
3
comment Is the set of all numbers which divide a specific function of their prime factors, infinite?
Can't find the commenting field, but here is the text of the problem from the contest. For a positive integer $n >1$ having a prime factorization $(p_1^{e_1}* p_2^{e_2}*p_3^{e_3}... *p_k^{e_k})$ define $f(n)= (p_1^{e_1+1}-1)(p_2^{e_2+1}-1)...(p_k^{e_k+1}-1)$. FInd an odd positive integer such that $n$ divides $f(n)$.
Feb
3
comment Interesting prime factorization function divisibility problem
I should clarify the intent of the question. What specifically about 819, say, makes it exactly fit the description of the function? I speak of careful mathematical observation as opposed to computation- something that could be done without a calculator. I saw this on a calculator-free set of questions I did last week and hadn't an idea about how to do it. The odd constraint made it especially difficult, as guessing and checking is futile in this problem. I know that n cannot be square free, but what observations of the mechanics of this function yields 819 in specific?
Feb
2
comment Interesting prime factorization function divisibility problem
What specifically about 819, say, makes it exactly fit the description of the function? I speak of careful mathematical observation as opposed to computation- something that could be done without a calculator. I saw this on a calculator-free contest I did last week and hadn't an idea about how to do it. The odd constraint made it especially difficult, as guessing and checking is futile in this problem. I know that n cannot be square free, but what observations of the mechanics of this function yields 819 in specific?
Feb
2
asked Pinwheel- perimeter of semicircular region
Feb
2
comment Interesting prime factorization function divisibility problem
Gerry- didn't see your comment @ the time. Thank you for the link.
Feb
2
answered In how many ways balls be distributed in boxes?
Feb
2
comment Is the set of all numbers which divide a specific function of their prime factors, infinite?
Raymond- what observations did you make to write the table? Did you use a program to brute force? What specifically about 819, say, makes it exactly fit the description? I speak of careful mathematical observation as opposed to computation- something that could be done without a calculator. I saw this on a calculator-free contest I did last week and hadn't an idea about how to do it. The odd constraint made it especially difficult, as guessing and checking is futile in this problem
Feb
2
asked Interesting prime factorization function divisibility problem
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2
asked Similar Right Triangles and Incircles
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