# [seqfan] Re: A066077

israel at math.ubc.ca israel at math.ubc.ca
Thu Dec 28 04:19:45 CET 2017

So it seems a correct description would be:

Number of x such that sigma(x)-1 is 0 or one of the first n-1 primes.

Cheers,
Robert

On Dec 27 2017, rgwv at rgwv.com wrote:

> It should be noticed that the sequence is always increasing. The first
> difference of A066077 seems to be A066075.
>
> -----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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