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A137324 a(n) = Sum_{prime p < n} gcd(n,p). 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 for prime p. - 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; 2 + 1 + 5 + 1 = 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

(MAGMA) [&+[Gcd(n, p):p in PrimesInInterval(1, n-1)]:n in [3..77]]; // Marius A. Burtea, Aug 07 2019

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 October 17 04:09 EDT 2019. Contains 328106 sequences. (Running on oeis4.)