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

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, 162, 128, 96, 108, 128, 144, 162, 256, 192, 216, 486, 256, 288, 324, 512, 384, 432, 486, 512, 576, 648, 1024, 1458, 768, 864, 972, 1024, 1152, 1296, 2048, 1458, 1536

Offset: 1

Author

Reinhard Zumkeller, Jul 18 2003

Keywords

• nonn

Comments

a(n) is 3-smooth.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Totient Function.
• Eric Weisstein's World of Mathematics, Smooth Number.

Crossrefs

Cf. A000010, A003586.

Programs

Mathematica

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 *)

Formula

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.

Sum_{n>=1} 1/a(n) = 21/4. - Amiram Eldar, Dec 21 2020