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

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

Offset: 1

Author

Ctibor O. Zizka, Nov 01 2008

Keywords

• nonn
• fini
• full

Comments

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

Crossrefs

Cf. A000027, A000005, A034884.

Programs

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

Extensions

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