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 A367865 #19 Dec 06 2023 08:34:09
%S A367865 1,3,7,3,21,21,43,3,7,63,111,21,157,129,147,3,273,21,343,63,301,333,
%T A367865 507,21,21,471,7,129,813,441,931,3,777,819,903,21,1333,1029,1099,63,
%U A367865 1641,903,1807,333,147,1521,2163,21,43,63,1911,471,2757,21,2331,129,2401,2439
%N A367865 a(n) = Sum_{d|n} d * phi(d) * mu(d)^2.
%C A367865 Inverse Möbius transform of n * phi(n) * mu(n)^2.
%H A367865 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%F A367865 Multiplicative with a(p^e) = p^2 - p + 1. - _Amiram Eldar_, Dec 04 2023
%F A367865 Sum_{k=1..n} a(k) ~ c * n^3/3, where c = Product_{p prime} (1 - 2/(1+p+p^2)) = 0.51478027457383523467921514707014858470711969900467102074735896602342984... - _Vaclav Kotesovec_, Dec 05 2023
%t A367865 Table[Sum[d*EulerPhi[d]*MoebiusMu[d]^2, {d, Divisors[n]}], {n, 100}]
%o A367865 (PARI) a(n) = sumdiv(n, d, if (issquarefree(d), d*eulerphi(d))); \\ _Michel Marcus_, Dec 04 2023
%o A367865 (Python)
%o A367865 from math import prod
%o A367865 from sympy import primefactors
%o A367865 def A367865(n): return prod(p*(p-1)+1 for p in primefactors(n)) # _Chai Wah Wu_, Dec 05 2023
%Y A367865 Cf. A000010 (phi), A007947 (rad), A008966 (mu^2), A202535.
%K A367865 nonn,easy,mult
%O A367865 1,2
%A A367865 _Wesley Ivan Hurt_, Dec 03 2023