A371241 Euler totient function applied to the zeroless numbers in base 3 (A032924).

1, 1, 2, 4, 6, 4, 12, 6, 8, 16, 10, 22, 20, 12, 16, 40, 42, 20, 42, 20, 24, 52, 66, 32, 24, 70, 36, 60, 78, 32, 110, 60, 60, 100, 48, 130, 108, 66, 72, 148, 150, 72, 156, 78, 64, 132, 100, 168, 160, 102, 210, 104, 106, 168, 228, 88, 112, 232, 96, 238, 240, 110

Offset: 1

Author

Amiram Eldar, Mar 16 2024

Keywords

• nonn
• base
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• William D. Banks and Igor E. Shparlinski, Arithmetic properties of numbers with restricted digits, Acta Arithmetica, Vol. 112, No. 4 (2004), pp. 313-332; alternative link.

Crossrefs

Cf. A000010, A032924, A214549, A371239, A371240.

Programs

Mathematica

EulerPhi[Select[Range[300], !MemberQ[IntegerDigits[#, 3], 0] &]]

PARI

lista(kmax) = for(k = 1, kmax, if(vecmin(digits(k, 3)) > 0, print1(eulerphi(k), ", ")));

Formula

a(n) = A000010(A032924(n)).

Asymptotic mean of phi(k)/k over A032924: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A032924(k) = 27/(4*Pi^2) = 1/A214549 = 0.683917... (Banks and Shparlinski, 2004).