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A133578
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.
3
4, 6, 9, 11, 14, 16, 16, 17, 22, 21, 20, 31, 23, 27, 36, 28, 43, 45, 37, 26, 51, 31, 57, 30, 29, 36, 41, 68, 31, 39, 29, 38, 51, 44, 56, 40, 101, 59, 101, 81, 106, 37, 41, 114, 37, 35, 74, 59, 141, 56, 56, 42, 40, 34, 64, 153, 87, 41, 171, 70, 127, 96, 47, 60, 181, 141, 108
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) = 6 - for prime 3
a(3) = (2+2) + (2+3) = 9 - for prime 5
a(4) = (2+3) + (2+2+2) = 11 - for prime 7
a(5) = (2+5) + (2+2+3) = 14 - for prime 11
MAPLE
A133578 := proc(n)
if n = 1 then
4;
else
A001414(ithprime(n)+1)+A001414(ithprime(n)-1) ;
fi ;
end:
seq(A133578(n), n=1..80) ; # R. J. Mathar, Jan 18 2008
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A122183 A234373 A189756 * A347467 A285078 A186318
KEYWORD
nonn,easy
AUTHOR
Alexander R. Povolotsky, Dec 30 2007, corrected Jan 03 2007
EXTENSIONS
Edited by N. J. A. Sloane, Jan 14 2007
More terms from R. J. Mathar and Stefan Steinerberger, Jan 18 2008
STATUS
approved