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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
OFFSET
1,1
LINKS
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
Sequence in context: A358476 A185304 A081389 * A281492 A112183 A275451
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