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

1,19

Links

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

Formula

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

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

Mathematica

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

Prog

(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.

Crossrefs

Cf. A000010, A007949, A074942.

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

Cf. also A354100.

Sequence in context: A123758 A231642 A288318 * A219483 A239927 A069846

Adjacent sequences: A354096 A354097 A354098 * A354100 A354101 A354102

Keyword

nonn

Author

Antti Karttunen, May 17 2022

Status

approved