cp's OEIS Frontend

A340179 a(n) = Sum_{x in C(n)} (A023896(n) mod x), where C(n) is the set of numbers < n coprime to n, and A023896(n) is the sum of C(n).

%I A340179 #18 Feb 03 2021 23:25:41
%S A340179 0,0,1,1,3,1,6,4,15,10,25,9,33,20,25,32,49,24,56,34,68,48,98,35,152,
%T A340179 54,100,89,180,30,178,91,146,146,150,115,314,160,220,166,315,120,306,
%U A340179 211,267,254,412,196,485,224,383,339,600,243,609,306,481,419,801,215,859,490,577,567,782,297,865
%N A340179 a(n) = Sum_{x in C(n)} (A023896(n) mod x), where C(n) is the set of numbers < n coprime to n, and A023896(n) is the sum of C(n).
%H A340179 Robert Israel, <a href="/A340179/b340179.txt">Table of n, a(n) for n = 1..10000</a>
%e A340179 For n=8, C = {1,3,5,7}, c = 1+3+5+7 = 16, and a(n) = (16 mod 1) + (16 mod 3) + (16 mod 5) + (16 mod 7) = 0+1+1+2 = 4.
%p A340179 f:= proc(n) local C,s,c;
%p A340179   C:=select(t -> igcd(t,n) = 1, [$1..n-1]);
%p A340179   s:= convert(C,`+`);
%p A340179   add(s mod c, c = C)
%p A340179 end proc:
%p A340179 map(f, [$1..100]);
%t A340179 Table[Total@ Mod[#2, #1] & @@ {#, Total@ #} &@ Select[Range[n], GCD[#, n] == 1 &], {n, 67}] (* _Michael De Vlieger_, Dec 31 2020 *)
%o A340179 (PARI) apply( {A340179(n,s=n*eulerphi(n)\/2)=sum(k=2,n-1,if(gcd(n,k)<2,s%k))}, [1..66]) \\ _M. F. Hasler_, Feb 01 2021
%Y A340179 Cf. A023896, A340180.
%K A340179 nonn,look
%O A340179 1,5
%A A340179 _J. M. Bergot_ and _Robert Israel_, Dec 30 2020