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%I #13 Feb 20 2017 00:26:44
%S 4,6,9,11,14,16,16,17,22,21,20,31,23,27,36,28,43,45,37,26,51,31,57,30,
%T 29,36,41,68,31,39,29,38,51,44,56,40,101,59,101,81,106,37,41,114,37,
%U 35,74,59,141,56,56,42,40,34,64,153,87,41,171,70,127,96,47,60,181,141,108
%N Let p = prime(n); then a(n) = (sum of prime factors of p+1) + (sum of prime factors of p-1). a(1) = 4 by convention.
%H G. C. Greubel, <a href="/A133578/b133578.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) = 6 - for prime 3
%e a(3) = (2+2) + (2+3) = 9 - for prime 5
%e a(4) = (2+3) + (2+2+2) = 11 - for prime 7
%e a(5) = (2+5) + (2+2+3) = 14 - for prime 11
%p A133578 := proc(n)
%p if n = 1 then
%p 4;
%p else
%p A001414(ithprime(n)+1)+A001414(ithprime(n)-1) ;
%p fi ;
%p end:
%p seq(A133578(n),n=1..80) ; # _R. J. Mathar_, Jan 18 2008
%t a = {4}; 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, A133685.
%K nonn,easy
%O 1,1
%A _Alexander R. Povolotsky_, Dec 30 2007, corrected Jan 03 2007
%E Edited by _N. J. A. Sloane_, Jan 14 2007
%E More terms from _R. J. Mathar_ and _Stefan Steinerberger_, Jan 18 2008
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