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.

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

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) = 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

Cf. A000040, A133685.

Sequence in context: A122183 A234373 A189756 * A347467 A285078 A186318

Adjacent sequences: A133575 A133576 A133577 * A133579 A133580 A133581

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