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 May 26 comment Amicable pair sums - intriguing sexagesimal relationships $\sigma(m)=\sigma(n) = m+n was meant May 26 comment Amicable pair sums - intriguing sexagesimal relationships Please help me out with te Riele's paper. He defines an amicable pair as$\sigma(m)=\sigma(n) = m+n, whereas I've understood it to be the sum of m's divisors equalling n, and n's equalling m. May 25 comment Amicable pair sums - intriguing sexagesimal relationships Most the pair sums I've looked at in response to your answer so far are smoother than either of the two numbers in the pair concerned, or at least have a greatest prime factor smaller than the average gpf of the two numbers. That is, if amicable sum m + n is k smooth, then k < (j+l)/2 iff m is j smooth and n is l smooth. Summing AP's seems to be a way of smoothing out, reducing the incidence of big lumpy primes. Getting lots of small ones instead: 2's, 3's, 5's, makes it less surprising to get multiples and powers of 6 and 10 so frequently. Apr 22 revised Is there any geometry where ratio of circle's circumference to its diameter is rational? added 22 characters in body Apr 22 answered Is there any geometry where ratio of circle's circumference to its diameter is rational? Mar 28 awarded Peer Pressure Mar 1 comment Split number in two, so that two rounded portions equal the original. The algebra simplifies things: 2((a/2)+b) is greater than a, where a and b are greater than 0. Feb 28 revised Split number in two, so that two rounded portions equal the original. deleted 10 characters in body Feb 28 revised Split number in two, so that two rounded portions equal the original. added 138 characters in body Feb 27 revised Split number in two, so that two rounded portions equal the original. added 15 characters in body Feb 27 revised Split number in two, so that two rounded portions equal the original. added 15 characters in body Feb 27 revised Split number in two, so that two rounded portions equal the original. added 15 characters in body Feb 27 revised Split number in two, so that two rounded portions equal the original. added 14 characters in body Feb 27 revised Split number in two, so that two rounded portions equal the original. added 77 characters in body Feb 27 revised Split number in two, so that two rounded portions equal the original. deleted 121 characters in body Feb 27 revised Split number in two, so that two rounded portions equal the original. added 182 characters in body Feb 27 answered Split number in two, so that two rounded portions equal the original. Feb 27 revised truth tables and validity of arguments edited body Feb 27 revised truth tables and validity of arguments added 156 characters in body Feb 26 revised truth tables and validity of arguments deleted 744 characters in body