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

Allan Wechsler acwacw at gmail.com
Mon Aug 12 20:11:39 CEST 2019

```An English restatement of Gerasimov's problem is:

Let A(n) be the exponent of 2 in the prime factorization of sigma(2^n - 1),
where sigma is the sum-of-divisors function.

Gerasimov asks, for what values of n does A(n) = n-1 ?

I was unable to find any other solutions besides Israel's two (and the
trivial n=1). But the sequence A(n) begins (with offset 1):

0,2,3,3,5,3,7,4,4,9,4,5,13,11,11...

This sequence does not appear in OEIS, but I could easily have made a
calculation error.

Note that A(n) = n exactly when n is a Mersenne exponent.

It looks to me like A(n) is usually much less than n; I would like to know
where Gerasimov gets his intuition that A(n)=n-1 has a lot of solutions.

On Mon, Aug 12, 2019 at 8:27 AM <israel at math.ubc.ca> wrote:

> How about x=3 and x=9?
>
> Cheers,
> Robert
>
> On Aug 11 2019, юрий герасимов wrote:
>
> > Although I suppose that the number of solutions to this equation is
> > numerically numerous, but I myself could not calculate at least one!
> Very
> >
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> >
> >
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```