A146567 Numbers k such that k*sigma_0(k)/(k+sigma_0(k)) = c, c an integer.

2, 12, 24, 56, 60, 132, 1260

Offset

1,1

Comments

A000027(k)*A000005(k)/(A000027(k)+A000005(k))=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(k)^2 < k for k > 1260 (see A034884). - Giovanni Resta, Sep 13 2015

Links

Table of n, a(n) for n=1..7.

Maple

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

Crossrefs

Cf. A000027, A000005, A034884.

Sequence in context: A051781 A077562 A307003 * A176679 A278407 A224923

Adjacent sequences: A146564 A146565 A146566 * A146568 A146569 A146570

Keyword

nonn,fini,full

Author

Ctibor O. Zizka, Nov 01 2008

Extensions

Corrected and extended (one term) by Emeric Deutsch, Nov 09 2008

Status

approved