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 A133685 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. 2
 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, -3, -42, 5, 9, -1, -2, 5, -12, -26, 10, 61, 31, -69, -13, -76, 7, -11, 84, 1, -3, 40, -25, -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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 FORMULA a(n) = A001414(A000040(n)+1)-A001414(A000040(n)-1), n>1. - R. J. Mathar, Jan 18 2008 EXAMPLE a(2) = (2+2) - 2 = 2 - for prime 3 a(3) = (2+3) - (2+2) = 1 - for prime 5 a(4) = (2+2+2) - (2+3) = 1 - for prime 7 a(5) = (2+2+3) - (2+5) = 0 - for prime 11 MAPLE 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 MATHEMATICA 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 *) CROSSREFS Cf. A000040, A133578. Sequence in context: A123736 A185304 A081389 * A281492 A112183 A275451 Adjacent sequences:  A133682 A133683 A133684 * A133686 A133687 A133688 KEYWORD easy,sign AUTHOR Alexander R. Povolotsky, Dec 31 2007, corrected Jan 03 2007 EXTENSIONS More terms from R. J. Mathar and Stefan Steinerberger, Jan 18 2008 STATUS approved

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Last modified September 25 06:32 EDT 2020. Contains 337335 sequences. (Running on oeis4.)