A190722 Primes p such that A008472(p-1) = A008472(p+1) and is a prime.

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

Offset: 1

Author

Robert G. Wilson v, May 17 2011

Keywords

• nonn

Comments

A008472 is the sum of the distinct primes dividing n.

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..223 (calculated from the b-file at A203182)

Crossrefs

Cf. A190680, A008472, A086711.

Subsequence of A203182.

Programs

Magma

[p:p in PrimesInInterval(3,10^8)|(&+PrimeDivisors(p-1) eq &+PrimeDivisors(p+1)) and IsPrime(&+PrimeDivisors(p-1))]; // Marius A. Burtea, Nov 14 2019

Mathematica

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@p, AppendTo[lst, p]; Print@p]; p =
NextPrime@p]; lst
pQ[n_]:=Module[{p1=Total[FactorInteger[n-1][[All,1]]],p2=Total[ FactorInteger[ n+1][[All,1]]]},p1==p2&&PrimeQ[p1]]; Select[ Prime[ Range[5*10^6]],pQ] (* Harvey P. Dale, Jun 18 2017 *)