# [seqfan] Re: reducing Devaraj non-Carmichel numbers in A164946

William Rex Marshall w.r.marshall at actrix.co.nz
Thu Dec 16 04:55:54 CET 2010

```On 16/12/2010 12:17 p.m., Richard Mathar wrote:

> First example is 11305 = 5*7*17*19, prime-factors are 4,6,16,18 after
> reduction, with gcd(4,6,16,18) = 2. So 2^2*(11305-1)^2/4/6/16/18 = 73947
> according to my interpretation.

That's not how the first term is calculated in the example listed in
A164946, which is

"The factors of the first member of A104017 (11305) are 5, 7, 17 and 19.
Hence the first term of the present sequence is (4*11304^2)/(6*16*18) =
295788"

which suggests to me that if the prime factorisation of A104017(n) is p
* q * r * ... * t (where p is the smallest prime factor) then a(n) =
((p-1) * A104017(n)^2) / ((q-1) * (r-1) * ... * (t-1)).

This formula reproduces all the terms listed in A164946, along with
a(11) = 107785924. The sequence then fractures at n=12 with the first
noninteger, 135008886.375 (or 135008886 3/8).

```