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Sum of coprimes of n greater than 1.
2

%I #26 Nov 12 2023 08:48:39

%S 0,0,0,2,3,9,5,20,15,26,19,54,23,77,41,59,63,135,53,170,79,125,109,

%T 252,95,249,155,242,167,405,119,464,255,329,271,419,215,665,341,467,

%U 319,819,251,902,439,539,505,1080,383,1028,499,815,623,1377,485,1099,671,1025

%N Sum of coprimes of n greater than 1.

%H Robert P. P. McKone, <a href="/A109607/b109607.txt">Table of n, a(n) for n = 0..14143</a>

%F a(n) = A023896(n) - 1. - _Joerg Arndt_, Mar 08 2013

%F G.f.: -x/(1 - x) + Sum_{k>=1} mu(k)*k*x^k/(1 - x^k)^3. - _Ilya Gutkovskiy_, May 28 2019

%e a(9) = 26 because 2,4,5,7,8 are coprime to 9 and 2+4+5+7+8 = 26.

%t a[n_] := Total@Select[Range[2, n], CoprimeQ[n, #] &]; Table[a[n], {n, 0, 57}] (* _Robert P. P. McKone_, Nov 12 2023 *)

%o (PARI) a(n) = sum(i=2, n-1, i*(gcd(i, n)==1)); \\ _Michel Marcus_, Mar 08 2013

%o (PARI) a(n)=if(n<3,0,n*eulerphi(n)/2-1) \\ _Charles R Greathouse IV_, Mar 08 2013

%Y Cf. A023896.

%K nonn,look

%O 0,4

%A _Andrew Weimholt_, Jul 31 2005

%E Added "greater than 1" to name to match terms, _Joerg Arndt_, Mar 08 2013