A067439 - OEIS

%I #18 Nov 06 2014 15:35:19

%S 0,0,1,1,4,1,8,6,9,5,22,8,28,15,19,20,51,20,64,30,39,33,98,33,83,56,

%T 89,55,151,46,167,95,107,95,150,71,233,120,172,106,297,92,325,163,186,

%U 162,403,144,358,189,279,217,505,173,375,230,342,276,635,165,645,338

%N a(n) = sum of all the remainders when n is divided by positive integers less than and coprime to n.

%H Charles R Greathouse IV, <a href="/A067439/b067439.txt">Table of n, a(n) for n = 1..10000</a>

%e a(8) = 6. The remainders when 8 is divided by the coprime numbers 1, 3, 5 and 7 are 0, 2, 3 and 1, whose sum = 6.

%t a[n_] := Sum[If[GCD[i, n]>1, 0, Mod[n, i]], {i, 1, n-1}]

%t Table[Total[Mod[n,#]&/@Select[Range[n-1],CoprimeQ[#,n]&]],{n,70}] (* _Harvey P. Dale_, May 22 2012 *)

%o (PARI) a(n)=sum(i=1,n-1,if(gcd(n,i)==1,n%i)) \\ _Charles R Greathouse IV_, Jul 17 2012

%Y Cf. A004125, A067435, A067436, A024934, A033955.

%K nonn

%O 1,5

%A _Amarnath Murthy_, Jan 29 2002

%E Edited by _Dean Hickerson_, Feb 15 2002