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A133685
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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.
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2
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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; internal format)
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OFFSET
| 1,1
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FORMULA
| a(n) = A001414(A000040(n)+1)-A001414(A000040(n)-1), n>1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 18 2008
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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
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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 (mathar(AT)strw.leidenuniv.nl), Jan 18 2008
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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 (stefan.steinerberger(AT)gmail.com), Jan 18 2008
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CROSSREFS
| Cf. A000040, A133578.
Sequence in context: A099860 A123736 A081389 * A112183 A119557 A125919
Adjacent sequences: A133682 A133683 A133684 * A133686 A133687 A133688
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KEYWORD
| easy,sign
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AUTHOR
| Alexander R. Povolotsky (pevnev(AT)juno.com), Dec 31 2007, corrected Jan 03 2007
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jan 18 2008
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