A133685 - OEIS

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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, 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

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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: A358476 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