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 A349338 #21 Jun 21 2025 11:50:14
%S A349338 1,2,3,3,5,5,7,6,8,9,11,8,13,13,14,12,17,14,19,14,20,21,23,16,24,25,
%T A349338 24,20,29,22,31,24,32,33,34,22,37,37,38,28,41,32,43,32,38,45,47,32,48,
%U A349338 44,50,38,53,42,54,40,56,57,59,36,61,61,54,48,64,52,67,50,68,58,71,44,73,73,68,56,76,62,79,56,72,81
%N A349338 Dirichlet convolution of A000010 (Euler totient phi) with A080339 (characteristic function of noncomposite numbers).
%C A349338 Möbius transform of A230593.
%C A349338 The number of integers k from 1 to n such that gcd(n, k) is a noncomposite number. - _Amiram Eldar_, Jun 21 2025
%H A349338 Antti Karttunen, <a href="/A349338/b349338.txt">Table of n, a(n) for n = 1..20000</a>
%F A349338 a(n) = Sum_{d|n} A000010(n/d) * A080339(d).
%F A349338 a(n) = Sum_{d|n} A008683(n/d) * A230593(d).
%F A349338 a(n) = Sum_{d|n} A349435(n/d) * A348976(d).
%F A349338 a(n) = A000010(n) + A117494(n). [Because A117494 is the Möbius transform of A069359]
%F A349338 For all n >= 1, a(A005117(n)) = A348976(A005117(n)).
%F A349338 Sum_{k=1..n} a(k) ~ 3 * (1 + A085548) * n^2 / Pi^2. - _Vaclav Kotesovec_, Nov 20 2021
%t A349338 a[n_] := DivisorSum[n, Boole[!CompositeQ[#]] * EulerPhi[n/#] &]; Array[a, 100] (* _Amiram Eldar_, Nov 17 2021 *)
%o A349338 (PARI) A349338(n) = sumdiv(n, d, eulerphi(n/d)*((1==d)||isprime(d)));
%o A349338 (PARI) a(n) = {my(f = factor(n), p = f[,1], e = f[,2]); n * vecprod(apply(x -> 1-1/x, p)) * (1 + vecsum(apply(x -> 1/x, p - vector(#e, i, e[i] == 1)~)));} \\ _Amiram Eldar_, Jun 21 2025
%Y A349338 Cf. A000010, A005117, A008683, A069359, A080339, A085548, A117494, A230593, A348976, A349435.
%K A349338 nonn
%O A349338 1,2
%A A349338 _Antti Karttunen_, Nov 17 2021