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#25 by Peter Luschny at Sat Apr 11 06:28:46 EDT 2020
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#24 by Joerg Arndt at Sat Apr 11 05:45:58 EDT 2020
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#23 by Michel Marcus at Sat Apr 11 00:41:36 EDT 2020
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#22 by Michel Marcus at Sat Apr 11 00:41:32 EDT 2020
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| COMMENTS
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Paul Erdöős and Leo Moser conjectured that, for any even numbers 2*n, there exist integers q and r such that phi(q) + phi(r) = 2*n. Therefore, they conjecture a(n) > 0 for all ns.
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| STATUS
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approved
editing
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#21 by N. J. A. Sloane at Thu Apr 09 22:24:43 EDT 2020
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#20 by Robert G. Wilson v at Thu Apr 09 22:20:03 EDT 2020
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#19 by Robert G. Wilson v at Thu Apr 09 22:19:59 EDT 2020
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| NAME
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a(n) is the number of unique solutionspairs (q,r) such that for some q & <= r withand q =< r, phi(q) + phi(r) = 2*n.
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#18 by N. J. A. Sloane at Thu Apr 09 20:51:26 EDT 2020
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#17 by Robert G. Wilson v at Tue Apr 07 15:14:11 EDT 2020
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Discussion
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| Tue Apr 07
| 15:15
| Robert G. Wilson v: They're fixed.
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| Thu Apr 09
| 20:51
| N. J. A. Sloane: Have you perhaps written "unique" when you meant to say "distinct" ? Even so, the definition does not really make sense. Why not simply say something like this: a(n) is the number of pairs (q,r) such that q =< r and phi(q) + phi(r) = 2*n. Also remember that one says <= not =<.
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#16 by Robert G. Wilson v at Tue Apr 07 15:14:07 EDT 2020
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| COMMENTS
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Paul Erdös and Leo Moser conjectured that, for any even numbers 2*n, there exist integers q and r such that phi(q) + phi(r) = 2*n. Therefore, they conjecture a(n) > 0 for all ns.
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| EXAMPLE
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a(2) = 6 because for the pairs {q, r} the following pairs when phi(q) + phi(r) = 4; {3,3},{}, {3,4},{}, {3,6},{}, {4,4},{}, {4,6},{}, {6,6}.
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