# [seqfan] Re: sum of prime factors of p-1 and p+1

RGWv rgwv at rgwv.com
Tue May 17 00:39:05 CEST 2011

```Neil,

Not counting multiplicity, the sequence is:

{3, 45751, 149351, 171529, 223099, 434237, 678077, 706841, 1996297, 3993037,
6340457, 7199113, 7419761, 9000317, 13129271, 15052777, 17193217, 18436879,
18749881, 18998519, 23353469, 23689423, 33746663, 40985411, 41437751,
43547797, 51198097, 53773651, 56825687, 60207809, 62190113, 79778899,
81708353, 83019421}
example, for p = 45751, p-1 = 2*3*5^3*61; 2+3+5+61=71 and p+1 = 2^3*7*19*43;
2+7+19+43 = 71.
fQ[n_] := Block[{pn = Plus @@ (First@# & /@ FactorInteger[n - 1]), pp = Plus
@@ (First@# & /@ FactorInteger[n + 1])}, pn == pp && PrimeQ[pn]];
p = 2; lst = {}; While[p < 10^8, If[fQ at p, AppendTo[lst, p]; Print at p]; p =
NextPrime at p]; lst

Sincerely yours, Bob.

-----Original Message-----
From: N. J. A. Sloane
Sent: Monday, May 16, 2011 4:43 PM
To: seqfan at seqfan.eu
Cc: njas at research.att.com
Subject: [seqfan] sum of prime factors of p-1 and p+1

Seq Fans, This just came in from a correspondent.
Can someone please compute further terms and submit it?
Neil

>From thekingfishb at yahoo.ca Mon May 16 13:51:01 2011
From: JM Bergot <thekingfishb at yahoo.ca>
Subject: A086715 & A001414

Primes p such that that for some prime q,
the sum of the prime factors of p-1 = q,
and the same for p+1:
11, 251 and 1429.

For 11 q is 7, for 251 it is 17, and for 1429 it is 31.

(end)

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/

```