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A374456 The Euler phi function values of the exponentially odd numbers (A268335).

%I A374456 #8 Jul 10 2024 02:58:15
%S A374456 1,1,2,4,2,6,4,4,10,12,6,8,16,18,12,10,22,8,12,18,28,8,30,16,20,16,24,
%T A374456 36,18,24,16,40,12,42,22,46,32,52,18,40,24,36,28,58,60,30,48,20,66,44,
%U A374456 24,70,72,36,60,24,78,40,82,64,42,56,40,88,72,60,46,72,32,96
%N A374456 The Euler phi function values of the exponentially odd numbers (A268335).
%H A374456 Amiram Eldar, <a href="/A374456/b374456.txt">Table of n, a(n) for n = 1..10000</a>
%F A374456 a(n) = A000010(A268335(n)).
%F A374456 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = A307868 / A065463^2 = 0.95051132596733153581... .
%t A374456 f[p_, e_] := If[OddQ[e], (p-1) * p^(e-1), 0]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Array[s, 100], # > 0 &]
%o A374456 (PARI) s(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] % 2, (f[i, 1]-1) * f[i, 1]^(f[i, 2] - 1), 0));}
%o A374456 lista(kmax) = {my(s1); for(k = 1, kmax, s1 = s(k); if(s1 > 0, print1(s1, ", ")));}
%Y A374456 Cf. A000010, A065463, A268335, A307868.
%Y A374456 Similar sequences related to phi: A002618, A049200, A323333, A358039.
%Y A374456 Similar sequences related to exponentially odd numbers: A366438, A366439, A366534, A366535, A367417, A368711, A374457.
%K A374456 nonn,easy
%O A374456 1,3
%A A374456 _Amiram Eldar_, Jul 09 2024