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).

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, 54, 100, 89, 180, 30, 178, 91, 146, 146, 150, 115, 314, 160, 220, 166, 315, 120, 306, 211, 267, 254, 412, 196, 485, 224, 383, 339, 600, 243, 609, 306, 481, 419, 801, 215, 859, 490, 577, 567, 782, 297, 865

Offset: 1

Author

J. M. Bergot and Robert Israel, Dec 30 2020

Keywords

• nonn
• look

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023896, A340180.

Programs

Maple

f:= proc(n) local C,s,c;
  C:=select(t -> igcd(t,n) = 1, [$1..n-1]);
  s:= convert(C,`+`);
  add(s mod c, c = C)
end proc:
map(f, [$1..100]);

Mathematica

Table[Total@ Mod[#2, #1] & @@ {#, Total@ #} &@ Select[Range[n], GCD[#, n] == 1 &], {n, 67}] (* Michael De Vlieger, Dec 31 2020 *)

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