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A380161 a(n) is the value of the Euler totient function when applied to the powerfree part of n.

%I A380161 #8 Jan 14 2025 01:51:41
%S A380161 1,1,2,1,4,2,6,1,1,4,10,2,12,6,8,1,16,1,18,4,12,10,22,2,1,12,1,6,28,8,
%T A380161 30,1,20,16,24,1,36,18,24,4,40,12,42,10,4,22,46,2,1,1,32,12,52,1,40,6,
%U A380161 36,28,58,8,60,30,6,1,48,20,66,16,44,24,70,1,72,36
%N A380161 a(n) is the value of the Euler totient function when applied to the powerfree part of n.
%H A380161 Amiram Eldar, <a href="/A380161/b380161.txt">Table of n, a(n) for n = 1..10000</a>
%F A380161 a(n) = A000010(A055231(n)).
%F A380161 a(n) >= 1, with equality if and only if n is in A335851.
%F A380161 a(n) <= A000010(n), with equality if and only if n is squarefree (A005117).
%F A380161 Multiplicative with a(p) = p-1, and a(p^e) = 1 if e >= 2.
%F A380161 Dirichlet g.f.: zeta(s) * Product_{p prime} (1 - 2/p^s + 1/p^(s-1) - 1/p^(2*s-1) + 2/p^(2*s)).
%F A380161 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(2) * Product_{p prime} (1 - 2/p^5 + 3/p^4 + 1/p^3 - 3/p^2) = 0.46288631864329056778... .
%t A380161 f[p_, e_] := If[e == 1, p-1, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A380161 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] == 1, f[i, 1]-1, 1));}
%Y A380161 Cf. A000010, A005117, A013661, A055231, A056671, A092261, A335851, A380160.
%K A380161 nonn,easy,mult
%O A380161 1,3
%A A380161 _Amiram Eldar_, Jan 13 2025