%I #12 Jan 21 2024 09:36:23
%S 0,1,4,8,16,21,36,44,60,73,100,104,144,157,180,208,256,261,324,328,
%T 376,421,484,476,560,601,648,680,784,765,900,912,984,1057,1108,1128,
%U 1296,1333,1396,1420,1600,1569,1764,1768,1836,1981,2116,2064,2268,2305,2436,2504,2704,2673
%N a(n) = Sum_{d|n} (n-d) * phi(n/d).
%C If p is prime, a(p) = Sum_{d|p} (p-d) * phi(p/d) = (p-1) * phi(p) + (p-p) * phi(1) = (p-1)^2.
%F a(n) = A000290(n) - A018804(n). - _Ridouane Oudra_, Jan 21 2024
%e a(6) = Sum_{d|6} (6-d) * phi(6/d) = 5*phi(6) + 4*phi(3) + 3*phi(2) + 0*phi(1) = 5*2 + 4*2 + 3*1 + 0*1 = 21.
%p with(numtheory): seq(add((n-d)*phi(n/d), d in divisors(n)), n=1..80); # _Ridouane Oudra_, Jan 21 2024
%t Table[Sum[(n - k)*EulerPhi[n/k^(1 - Ceiling[n/k] + Floor[n/k])] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 80}]
%o (PARI) a(n) = sumdiv(n, d, (n-d) * eulerphi(n/d)); \\ _Michel Marcus_, May 21 2021
%Y Cf. A000010, A000290, A018804.
%K nonn
%O 1,3
%A _Wesley Ivan Hurt_, May 20 2021