This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A344485 #18 Jul 16 2025 21:51:23
%S A344485 0,1,4,8,16,21,36,44,60,73,100,104,144,157,180,208,256,261,324,328,
%T A344485 376,421,484,476,560,601,648,680,784,765,900,912,984,1057,1108,1128,
%U A344485 1296,1333,1396,1420,1600,1569,1764,1768,1836,1981,2116,2064,2268,2305,2436,2504,2704,2673
%N A344485 a(n) = Sum_{d|n} (n-d) * phi(n/d).
%C A344485 a(n) is the sum of the (n - 1)-th antidiagonal in A074712. - _Ctibor O. Zizka_, Mar 14 2025
%C A344485 Möbius transform of A189835(n). - _Wesley Ivan Hurt_, Jul 16 2025
%F A344485 a(n) = A000290(n) - A018804(n). - _Ridouane Oudra_, Jan 21 2024
%F A344485 From _Wesley Ivan Hurt_, Jul 16 2025: (Start)
%F A344485 a(n) = Sum_{d|n} A189835(d) * mu(n/d).
%F A344485 a(p^k) = p^(2*k)-p^k-k*p^k+k*p^(k-1) for p prime and k>=1. (End)
%e A344485 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 A344485 with(numtheory): seq(add((n-d)*phi(n/d), d in divisors(n)), n=1..80); # _Ridouane Oudra_, Jan 21 2024
%t A344485 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 A344485 (PARI) a(n) = sumdiv(n, d, (n-d) * eulerphi(n/d)); \\ _Michel Marcus_, May 21 2021
%Y A344485 Cf. A000010, A000290, A018804, A074712, A189835.
%K A344485 nonn
%O A344485 1,3
%A A344485 _Wesley Ivan Hurt_, May 20 2021