A341063 a(n) = Sum_{i+j<=m+1} t_i * t_j, where t_1 < ... < t_m are the totatives of n.

1, 1, 5, 7, 35, 11, 126, 70, 177, 90, 715, 142, 1365, 357, 680, 876, 3876, 645, 5985, 1300, 2856, 2255, 12650, 1916, 11675, 4446, 11061, 5362, 31465, 3260, 40920, 12376, 18920, 13192, 30240, 9066, 82251, 20691, 37752, 19080, 123410, 13062, 148995, 34870, 52080, 44781, 211876, 27640, 186102, 45650

Offset: 1

Author

J. M. Bergot and Robert Israel, Feb 04 2021

Keywords

• nonn

Comments

The totatives of n are the numbers k <= n with gcd(k,n) = 1.

If p is prime, a(p) = (p+2)*(p+1)*p*(p-1)/24.

It appears that 12*a(n) is always a multiple of n.

Conjecture: if p and q are distinct primes, a(p*q) = (p^2-p)*(q^2-q)*(p^2*q^2-p^2*q-p*q^2+p*q+2*p+2*q)/24.

Examples

			The totatives of 8 are 1, 3, 5, 7, so a(8) = 1*(1+3+5+7)+3*(1+3+5)+5*(1+3)+7*1 = 70.
		

Links

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

Crossrefs

Cf. A038566.

Programs

Maple

f:= proc(n) local C,i,S,t;
  C:= select(t -> igcd(t,n)=1, [$1..n]);
  S:= ListTools:-PartialSums(C);
  add(S[-i]*C[i], i=1..nops(C))
end proc:
map(f, [$1..100]);