A122255 Characteristic function of numbers with 3-smooth Euler's totient (A000010).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1

Offset

1,1

Comments

Multiplicative because A000010 is. - Andrew Howroyd, Aug 01 2018

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for characteristic functions

Formula

a(n) = if A006530(A000010(n)) <= 3 then 1 else 0.

a(A122254(n)) = a(A048135(n)) = 1; a(A048136(n)) = 0.

a(n) = if n=1 then 0 else A122256(n) - A122256(n-1).

a(n) = A122261(n) for n < 25.

a(n) = A065333(A000010(n)). - Antti Karttunen, Aug 22 2017

Multiplicative with a(p^e) = 1 for e = 1 and A006530(p-1) <= 3 or p <= 3; otherwise 0. - Andrew Howroyd, Aug 01 2018

Example

For n = 25, phi(25) = 20 = 2^2 * 5^1, and this is not 3-smooth, thus a(25) = 0.
For n = 26, phi(26) = 12 = 2^4 * 3^1, and here there are no larger prime factors than 3 (12 is 3-smooth), thus a(26) = 1. - Antti Karttunen, Aug 22 2017

Mathematica

a[n_] := Boole[FactorInteger[EulerPhi[n]][[-1, 1]] <= 3];
a /@ Range[1, 100] (* Jean-François Alcover, Sep 20 2019 *)

Prog

(PARI) a(n)=n=eulerphi(n); n>>=valuation(n, 2); n==3^valuation(n, 3) \\ Charles R Greathouse IV, Feb 21 2013

Crossrefs

Cf. A000010, A006530, A065333, A122261, A122256 (partial sums).

Characteristic function of A122254.

Sequence in context: A334946 A225595 A228813 * A122261 A015120 A015142

Adjacent sequences: A122252 A122253 A122254 * A122256 A122257 A122258

Keyword

nonn,mult

Author

Reinhard Zumkeller, Aug 29 2006

Status

approved