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%I #10 Feb 20 2017 23:10:48
%S 2,2,1,1,0,2,0,1,-4,-1,0,11,1,3,-14,-6,-19,21,5,-2,27,-5,-29,-4,3,8,
%T -3,-42,5,9,-1,-2,5,-12,-26,10,61,31,-69,-13,-76,7,-11,84,1,-3,40,-25,
%U -89,4,-14,-10,8,0,32,-113,-55,9,111,34,23,-58,-3,-16,137,-25,66,10,-139,-17,43,-164,-35,-8,10,-176,-78,180,54,22
%N Let p = prime(n); then a(n) = (sum of prime factors of p+1) - (sum of prime factors of p-1). a(1) = 2 by convention.
%H G. C. Greubel, <a href="/A133685/b133685.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A001414(A000040(n)+1)-A001414(A000040(n)-1), n>1. - _R. J. Mathar_, Jan 18 2008
%e a(2) = (2+2) - 2 = 2 - for prime 3
%e a(3) = (2+3) - (2+2) = 1 - for prime 5
%e a(4) = (2+2+2) - (2+3) = 1 - for prime 7
%e a(5) = (2+2+3) - (2+5) = 0 - for prime 11
%p A001414 := proc(n) local ifs; ifs := ifactors(n)[2] ; add(op(1,i)*op(2,i),i=ifs) ; end: A133685 := proc(n) if n = 1 then 2; else A001414(ithprime(n)+1)-A001414(ithprime(n)-1) ; fi ; end: seq(A133685(n),n=1..80) ; # _R. J. Mathar_, Jan 18 2008
%t a = {2}; b[n_] := Sum[FactorInteger[n][[i, 1]]*FactorInteger[n][[i, 2]], {i, 1, Length[FactorInteger[n]]}];; Do[AppendTo[a, b[Prime[n] + 1] - b[Prime[n] - 1]], {n, 2, 70}]; a (* _Stefan Steinerberger_, Jan 18 2008 *)
%Y Cf. A000040, A133578.
%K easy,sign
%O 1,1
%A _Alexander R. Povolotsky_, Dec 31 2007, corrected Jan 03 2007
%E More terms from _R. J. Mathar_ and _Stefan Steinerberger_, Jan 18 2008
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