[seqfan] Re: ;x = A001511(A051027(A000079(x))).

[Antti Karttunen]

On 8/13/19, Hans Havermann <gladhobo at bell.net> wrote:
> I'm confused. I took the function to be A001511(A051027(A000079(x))) and its
> sought-for value x (ignoring the ; in front of the x as a typo). As such I
> found no solutions. Robert Israel suggested x=3 (where the function is 4)
> and x=9 (where the function is 10) and Allan Wechsler doubled down on that
> interpretation (that we are looking for instances where the function is
> x+1). Perhaps this involves the offset of A000079 being zero while the other
> two sequences have offset one. What am I missing?
>

Yes, I think people have introduced off-one error at some point.

Unraveling Juri's equation, I get this:
As A051027(n) = A000203(A000203(n)), and sigma(2^n) = 2^(1+n) - 1,
it means that we are searching for:

Numbers k such that valuation_2(sigma(2^(1+k) - 1)) = k-1, i.e.,
numbers k for which sigma(2^(1+k) - 1) = 2^(k-1) * t, for some odd t.

And thus, k=3 and k=9 are not in that set.


Best regards,

Antti