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Prime numbers p where d(p-1) = d(p+1) increases to a record.
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%I #21 Oct 30 2015 10:15:51

%S 7,19,41,199,919,5741,18089,41651,90271,446081,1276001,27033161,

%T 43220449,53308529,109245401,512669249,663929729,2266639649,

%U 2560742911,2969200961,8505402751,32540473601,61573368401,74335064959,109494811999

%N Prime numbers p where d(p-1) = d(p+1) increases to a record.

%C a(26) <= 354208192001. - _Donovan Johnson_, Jun 03 2011

%e a(1) = 7 because 7 is prime and d(6) = 4 = d(8).

%t s = Select[Prime@ Range@ 1000000, DivisorSigma[0, # - 1] == DivisorSigma[0, # + 1] &]; t = DivisorSigma[0, # - 1] & /@ s; a = {0}; b = {0}; Do[If[t[[k]] > Max@ b, AppendTo[a, s[[k]]]]; AppendTo[b, t[[k]]], {k, Length@ s}]; a (* _Michael De Vlieger_, Oct 30 2015 *)

%o (PARI) r=0; forprime(p=2,4e9,t=numdiv(p-1);if(t>r&t==numdiv(p+1),r=t; print1(p", "))) \\ _Charles R Greathouse IV_, May 27 2011

%Y Cf. A145337, A190646 (numbers n such that d(n-1)=d(n+1) increases to a record).

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, May 21 2011

%E a(14)-a(21) from _Charles R Greathouse IV_, May 27 2011

%E a(22) from _Charles R Greathouse IV_, May 31 2011

%E a(23)-a(25) from _Donovan Johnson_, Jun 03 2011