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Search: id:A137324
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| A137324 |
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Sum of GCD(n,k) for k = 1 to n-1, k prime. |
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+0
1
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| 1, 3, 2, 6, 3, 5, 6, 9, 4, 8, 5, 13, 12, 7, 6, 10, 7, 13, 16, 19, 8, 12, 13, 22, 11, 16, 9, 17, 10, 12, 23, 28, 21, 14, 11, 31, 26, 17, 12, 22, 13, 25, 20, 37, 14, 18, 21, 20, 33, 28, 15, 19, 30, 23, 36, 45, 16, 24, 17, 49, 26, 19, 34, 31, 18, 36, 43, 30, 19, 23, 20, 58, 27, 40, 37
(list; graph; listen)
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OFFSET
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3,2
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FORMULA
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a(p)=A000720(p)-1 where p denotes some prime. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 09 2008
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EXAMPLE
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a(10) = 9 because GCD(10,2) = 2, GCD(10,3) = 1, GCD(10,5)= 5, GCD(10,7) = 1, add them up to get 9.
The underlying irregular table of gcd(n,2), gcd(n,3), gcd(n,5), gcd(n,7) etc, for which a(n) provides row sums, is obtained by deleting columns from A050873(n,k), and looks as follows for n=3,4,5,...:
1
2 1
1 1
2 3 1
1 1 1
2 1 1 1
1 3 1 1
2 1 5 1
1 1 1 1
2 3 1 1 1
1 1 1 1 1
2 1 1 7 1 1
1 3 5 1 1 1
2 1 1 1 1 1
1 1 1 1 1 1
2 3 1 1 1 1 1
1 1 1 1 1 1 1
2 1 5 1 1 1 1 1
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MAPLE
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A137324 := proc(n) local a, i; a :=0 ; for i from 1 to numtheory[pi](n-1) do a := a+gcd(n, ithprime(i)) ; od: a; end: seq(A137324(n), n=3..80) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 09 2008
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MATHEMATICA
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Table[Plus @@ GCD[n, Select[Range[n - 1], PrimeQ[ # ] &]], {n, 3, 70}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 09 2008
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CROSSREFS
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Cf. A006579.
Adjacent sequences: A137321 A137322 A137323 this_sequence A137325 A137326 A137327
Sequence in context: A077880 A131969 A058971 this_sequence A011209 A071018 A038572
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KEYWORD
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easy,nonn
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AUTHOR
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Max Sills (maxwell.sills(AT)case.edu), Apr 06 2008
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 09 2008
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