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A122255 Characteristic function of numbers with 3-smooth Euler's totient (A000010). 5
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 (list; graph; refs; listen; history; text; internal format)
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

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: A152066 A225595 A228813 * A122261 A014922 A014988

Adjacent sequences:  A122252 A122253 A122254 * A122256 A122257 A122258

KEYWORD

nonn,mult

AUTHOR

Reinhard Zumkeller, Aug 29 2006

STATUS

approved

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Last modified April 26 12:00 EDT 2019. Contains 322472 sequences. (Running on oeis4.)