A354099 The 3-adic valuation of Euler totient function phi.

0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 0, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 1, 1, 2, 2, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 2, 0, 0, 0, 1, 1, 2, 0, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 0, 2, 1, 1, 1, 0, 3, 0, 0, 1, 0, 1, 0, 0, 0, 1, 2, 0, 1, 0, 2, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1

Offset: 1

Author

Antti Karttunen, May 17 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000010, A007949, A074942.

Cf. A088232 (positions of zeros), A066498 (of terms > 0).

Cf. also A354100.

Programs

Mathematica

a[n_] := IntegerExponent[EulerPhi[n], 3]; Array[a, 100] (* Amiram Eldar, May 17 2022 *)

PARI

A354099(n) = valuation(eulerphi(n),3);

PARI

A354099(n) = { my(f=factor(n)); sum(k=1,#f~,valuation((f[k,1]-1)*(f[k,1]^(f[k,2]-1)), 3)); }; \\ Demonstrates the additivity.

Formula

a(n) = A007949(A000010(n)).

Additive with a(p^e) = A007949((p-1)*p^(e-1)).