

A137324


Sum of GCD(n,k) for k = 1 to n1, 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
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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](n1) 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, n1, 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



