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 A137324 Sum of GCD(n,k) for k = 1 to n-1, k prime. 1
 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; refs; listen; history; text; internal format)
 OFFSET 3,2 LINKS FORMULA a(p) = A000720(p)-1 where p denotes some prime. - R. J. Mathar, Apr 09 2008 EXAMPLE 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 MAPLE 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, Apr 09 2008 MATHEMATICA Table[Plus @@ GCD[n, Select[Range[n - 1], PrimeQ[ # ] &]], {n, 3, 70}] (* Stefan Steinerberger, Apr 09 2008 *) PROG (PARI) a(n) = sum(k=1, n-1, gcd(n, k)*isprime(k)); \\ Michel Marcus, Nov 07 2014 CROSSREFS Cf. A006579. Sequence in context: A131969 A058971 A186204 * A011209 A182649 A257698 Adjacent sequences:  A137321 A137322 A137323 * A137325 A137326 A137327 KEYWORD easy,nonn AUTHOR Max Sills, Apr 06 2008 EXTENSIONS Corrected and extended by R. J. Mathar and Stefan Steinerberger, Apr 09 2008 STATUS approved

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Last modified December 10 20:55 EST 2018. Contains 318049 sequences. (Running on oeis4.)