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 Nov26 asked Question about set notation Feb19 awarded Teacher Feb18 revised Is it A Good Idea To Write Papers With Mathematica? added 123 characters in body Feb18 answered Is it A Good Idea To Write Papers With Mathematica? Feb18 awarded Commentator Feb16 awarded Supporter Feb16 awarded Scholar Feb16 accepted Cards and probability Feb3 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 $f(n)$. Feb3 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? Feb2 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? Feb2 asked Pinwheel- perimeter of semicircular region Feb2 comment Interesting prime factorization function divisibility problem Gerry- didn't see your comment @ the time. Thank you for the link. Feb2 answered In how many ways balls be distributed in boxes? Feb2 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 Feb2 asked Interesting prime factorization function divisibility problem Feb2 awarded Editor Feb2 revised Similar Right Triangles and Incircles edited tags Feb2 asked Similar Right Triangles and Incircles Feb2 awarded Student