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A146567
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Numbers n such that n*sigma_0(n)/(n+sigma_0(n)) = c, c an integer.
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2
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OFFSET
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1,1
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COMMENTS
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A000027(n)*A000005(n)/(A000027(n)+A000005(n))=c, c an integer.
No other term < 5000000. - Emeric Deutsch, Nov 09 2008
No other term < 10000000. - Michel Marcus, Jun 02 2013
For a given n let x be the minimal natural number such that n*x/(n+x)=c. I conjecture: from a certain n onward, x>sigma_0(n) for all n. Thus, there is no other solution bigger than 1260, and this sequence is finite. - Ctibor O. Zizka, Sep 13 2015
This sequence is complete. The finiteness proof is analogous to that of A152491, after observing that sigma_0(n)^2 < n for n > 1260 (see A034884). - Giovanni Resta, Sep 13 2015
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LINKS
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Table of n, a(n) for n=1..7.
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MAPLE
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with(numtheory): a:=proc (n) if type(n*tau(n)/(n+tau(n)), integer) = true then n else end if end proc: seq(a(n), n=1..200000); # Emeric Deutsch, Nov 09 2008
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CROSSREFS
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Cf. A000027, A000005, A034884.
Sequence in context: A051781 A077562 A307003 * A176679 A278407 A224923
Adjacent sequences: A146564 A146565 A146566 * A146568 A146569 A146570
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KEYWORD
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nonn,fini,full
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AUTHOR
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Ctibor O. Zizka, Nov 01 2008
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EXTENSIONS
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Corrected and extended (one term) by Emeric Deutsch, Nov 09 2008
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STATUS
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approved
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