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

1,5

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A023896, A340180.

Sequence in context: A210841 A007383 A206434 * A120394 A371667 A016575

Adjacent sequences: A340176 A340177 A340178 * A340180 A340181 A340182

Keyword

nonn,look

Author

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

Status

approved