[seqfan] Re: Boris Stechkin and A055004

[Felix Fröhlich]

Making old number theory texts available to registered users of the OEIS
sounds very interesting to me. I even could contribute an old paper myself
that is not accessible online and referenced in three OEIS sequences (the
1913 paper of Meissner referenced in the sequences that turn up when
searching for
https://oeis.org/search?q=%22die+teilbarkeit+von%22&language=english&go=Search).
I am a bit hesitant to upload it to the OEIS and link it in the respective
sequences, as the copyright status of that paper is unclear to me.

2016-06-03 6:32 GMT+02:00 Zak Seidov <seqfan at list.seqfan.eu>:

>  BTW The long-standing Q of mine:
> Is it any way to make some classical texts on NT
> *as, e.g., R. K. Guy, Unsolved Problems in Number Theory
> available (free! online!) at least to registered users of OEIS.
>
>
>
> >Пятница,  3 июня 2016, 4:33 +03:00 от israel at math.ubc.ca:
> >
> >A055004 is titled "Boris Stechkin's function". It has a reference to R. K.
> >Guy, Unsolved Problems Number Theory, A17. No formula is given, but
> >according to the Maple code (which does match the Data) it would be
> >
> >a(n) = Sum_{m=2..n} (m-1)*floor(n*(m-1)/m).
> >
> >But this definition doesn't seem to match anything stated in A17 of
> >"Unsolved Problems in Number Theory", which instead quotes three theorems
> >of Boris Stechkin referring to the function
> >
> >S(n) = # {m: 2 <= m <= n, (m-1) | floor(n(m-1)/m)}
> >
> >For example, the first is that n-1 is prime iff S(n) = d(n), the number of
> >divisors of n.
> >
> >This function S would produce (for 0 <= n <= 100) 0, 0, 1, 2, 3, 3, 4, 4,
> >4, 5, 5, 4, 6, 6, 4, 6, 7, 5, 6, 6, 6, 8, 6, 4, 8, 9, 5, 6, 8, 6, 8, 8, 6,
> >8, 6, 6, 11, 9, 4, 6, 10, 8, 8, 8, 6, 10, 8, 4, 10, 11, 7, 8, 8, 6, 8, 10,
> >10, 10, 6, 4, 12, 12, 4, 8, 11, 9, 10, 8, 6, 8, 10, 8, 12, 12, 4, 8, 10,
> 8,
> >10, 8, 10, 13, 7, 4, 12, 14, 6, 6, 10, 8, 12, 14, 8, 8, 6, 6, 14, 12, 6,
> >10, 13
> >
> >which does not seem to be in OEIS. I think it should be. But what to do
> >about A055004? It's an old sequence, so we shouldn't change the Data. Is
> >there a reference to this as a function of Stechkin? Does it have any
> >relationship to be primes?
> >
> >Cheers,
> >Robert
> >
> >--
> >Seqfan Mailing list -  http://list.seqfan.eu/
>
>
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