A086420 - OEIS

%I #13 Dec 21 2020 02:24:02

%S 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 162,128,96,108,128,144,162,256,192,216,486,256,288,324,512,384,432,

%U 486,512,576,648,1024,1458,768,864,972,1024,1152,1296,2048,1458,1536

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

%C a(n) is 3-smooth.

%H Amiram Eldar, <a href="/A086420/b086420.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SmoothNumber.html">Smooth Number</a>.

%F 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 Sum_{n>=1} 1/a(n) = 21/4. - _Amiram Eldar_, Dec 21 2020

%t 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 Cf. A000010, A003586.

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Jul 18 2003