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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

Table of n, a(n) for n=3..77.

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.)