a question about A134865

[Max Alekseyev]

On Mon, May 19, 2008 at 2:00 PM, David W. Wilson <wilson.d at anseri.com> wrote:

> I have a sneaking suspicion that A134865 might in fact be finite.

Just a side note.

It is strange that A005179 is not referred to in the description of A134865.
Each element of A134865 is an element of A005179 (i.e., the terms of
A134865 form a subset of the terms of A005179), and the definition can
be stated simply as: n is in A134865 iff for every divisor d of n,
A134865(A000005(d)) (= A140635(d)) is also a divisor of n.

So, the question of finiteness of A134865 is closely related to the
form of elements of A005179.

Regards,
Max

P.S. A140635 is a new sequence:

%I A140635
%S A140635 1, 2, 2, 4, 2, 6, 2, 6, 4, 6, 2, 12, 2, 6, 6, 16, 2, 12, 2,
12, 6, 6, 2, 24, 4, 6, 6, 12, 2, 24, 2, 12, 6, 6, 6, 36, 2, 6, 6, 24,
2, 24, 2, 12, 12, 6, 2, 48, 4, 12, 6, 12, 2, 24, 6, 24, 6, 6, 2, 60,
2, 6, 12, 64, 6, 24, 2, 12, 6, 24, 2, 60, 2, 6, 12, 12, 6, 24, 2, 48,
16, 6, 2, 60, 6, 6, 6, 24, 2, 60, 6, 12, 6, 6, 6, 60, 2, 12, 12, 36
%N A140635 The minimum positive integer having the same number of divisors as n.
%C A140635 Clearly, a(n)<=n for all n. Moreover, a(n)=n if and only
if n belongs to A005179.
%F A140635 a(n) = A005179(A000005(n))
%Y A140635 A000005, A005179
%O A140635 1
%K A140635 ,nonn,
%A A140635 Max Alekseyev (maxal at cs.ucsd.edu), May 19 2008