# [seqfan] Re: A066077

Neil Sloane njasloane at gmail.com
Thu Dec 28 02:42:41 CET 2017

```I think this is a case where we have to change the data to
fit the definition.  There's no other solution.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Email: njasloane at gmail.com

On Wed, Dec 27, 2017 at 8:19 PM, <rgwv at rgwv.com> wrote:

> f[n_] := Block[{k = 1, p = 1 + Prime at n}, While[DivisorSigma[1, k] != p,
> k++]; k]; Array[f, 70]   supports Robert's data, but not A066077. Bob.
>
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of
> israel at math.ubc.ca
> Sent: Wednesday, 27 December, 2017 7:15 PM
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] A066077
>
> A066077 is "Smallest x such that p(n) = Sigma[x] - 1."
> I don't know why the strange mix of [] and (), but I would have assumed
> Sigma[x] is A000203(x) and p(n) is A000040(n), and the Formula seems to
> confirm that.  But this doesn't match the Data at all.
> The Data are
>
> 1, 2, 3, 4, 5, 7, 8, 10, 11, 14, 15, 17, 18, 21, 22, 25, 27, 30, 31, 32,
> 37, 38, 40, 43, 46, 48, 49, 51, 53, 54, 56, 58, 60, 61, 63, 64, 66, 67, 68,
> 74, 75, 79, 81, 86, 87, 88, 89, 90, 93, 96, 97, 100, 107, 108, 114, 115,
> 117, 120, 122, 123, 124, 125, 128, 130, 134, 135
>
> and the values of A000203 corresponding to each of these are
>
> 1, 3, 4, 7, 6, 8, 15, 18, 12, 24, 24, 18, 39, 32, 36, 31, 40, 72, 32, 63,
> 38, 60, 90, 44, 72, 124, 57, 72, 54, 120, 120, 90, 168, 62, 104, 127, 144,
> 68, 126, 114, 124, 80, 121, 132, 120, 180, 90, 234, 128, 252, 98, 217, 108,
> 280, 240, 144, 182, 360, 186, 168, 224, 156, 255, 252, 204, 240
>
> which seem to have no relation to prime(n)+1, except that they are never
> equal!
>
> The sequence that matches the definition would start
>
> 2, 3, 5, 7, 6, 13, 10, 19, 14, 29, 21, 37, 20, 43, 33, 34, 24, 61, 67, 30,
> 73, 57, 44, 40, 52, 101, 63, 85, 109, 74, 93, 86, 137, 76, 149, 111, 157,
> 163, 60, 173, 88, 117, 105, 193, 197, 199, 211, 84, 147, 229, 90, 114, 241,
> 96, 257, 215, 136, 201, 277, 281, 283, 164, 172, 126, 313, 317, 331, 337,
> 347, 349, 353, 120, 367, 373, 379, 186, 261, 397, 401, 409, 236, 421, 230,
> 208, 327, 365, 232, 457, 461, 463, 198, 168, 487, 326, 499, 204, 509, 346,
> 523, 541
>
> and this seems not to be in OEIS.
>
> So what's going on here?  What is A066077 really?
>
> Cheers,
> Robert
>
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```