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Search: id:A133578
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| A133578 |
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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) = 4 by convention. |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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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
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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
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MAPLE
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A001414 := proc(n) local ifs; ifs := ifactors(n)[2] ; add(op(1, i)*op(2, i), i=ifs) ; end: 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 (mathar(AT)strw.leidenuniv.nl), Jan 18 2008
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MATHEMATICA
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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 (stefan.steinerberger(AT)gmail.com), Jan 18 2008
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CROSSREFS
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Cf. A000040, A133685.
Sequence in context: A060106 A094550 A122183 this_sequence A010387 A010411 A047209
Adjacent sequences: A133575 A133576 A133577 this_sequence A133579 A133580 A133581
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KEYWORD
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nonn,easy
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AUTHOR
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Alexander R. Povolotsky (pevnev(AT)juno.com), Dec 30 2007, corrected Jan 03 2007
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EXTENSIONS
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Edited by njas, Jan 14 2007
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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