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A086420 Euler's totient of 3-smooth numbers: a(n) = A000010(A003586(n)).

%I A086420 #14 Feb 16 2025 08:32:50
%S A086420 1,1,2,2,2,4,6,4,8,6,8,18,16,12,16,18,32,24,54,32,36,64,48,54,64,72,
%T A086420 162,128,96,108,128,144,162,256,192,216,486,256,288,324,512,384,432,
%U A086420 486,512,576,648,1024,1458,768,864,972,1024,1152,1296,2048,1458,1536
%N A086420 Euler's totient of 3-smooth numbers: a(n) = A000010(A003586(n)).
%C A086420 a(n) is 3-smooth.
%H A086420 Amiram Eldar, <a href="/A086420/b086420.txt">Table of n, a(n) for n = 1..10000</a>
%H A086420 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>.
%H A086420 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmoothNumber.html">Smooth Number</a>.
%F A086420 n>1: a(n) = A003586(n) * (if A003586(n) mod 3 > 0 then 1/2 else (1 + A003586(n) mod 2)/3), a(1) = 1.
%F A086420 Sum_{n>=1} 1/a(n) = 21/4. - _Amiram Eldar_, Dec 21 2020
%t A086420 s = {}; m = 12; Do[n = 3^k; While[n <= 3^m, AppendTo[s, n]; n*=2], {k, 0, m}]; EulerPhi /@ Union[s] (* _Amiram Eldar_, Jan 29 2020 *)
%Y A086420 Cf. A000010, A003586.
%K A086420 nonn
%O A086420 1,3
%A A086420 _Reinhard Zumkeller_, Jul 18 2003