[seqfan] Egyptian fractions over the primes A165558

Richard Mathar mathar at strw.leidenuniv.nl
Mon Sep 28 20:41:35 CEST 2009


For those who like puzzles, here is one tightly related to extending
http://research.att.com/~njas/sequences/A165558 non-trivially:
How can the number 2 be decomposed into a sum over distinct weighted inverse primes?
I.e., find solutions to
2 = e_1/p_1 + e_2/p_2 +e_3/p_3 +...
where p_i are a set of distinct primes, and e_i >=1 is a set of associated
integers (which ultimately play the role of prime powers in A165558).
The case 2 = 4/2 with p_1=2 and e_1=4 is so far the only case shown in A165558 which
is not of the "trivial" kind of selecting e_i=p_i, i=1,2, for an arbitrary set of 2 distinct primes.
(This may already have been answered somewhere else, for example in the OEIS.. )


Richard




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