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%I A122255 #22 Sep 20 2019 07:53:30
%S A122255 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,
%T A122255 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,
%U A122255 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
%N A122255 Characteristic function of numbers with 3-smooth Euler's totient (A000010).
%C A122255 Multiplicative because A000010 is. - _Andrew Howroyd_, Aug 01 2018
%H A122255 Antti Karttunen, <a href="/A122255/b122255.txt">Table of n, a(n) for n = 1..10000</a>
%H A122255 <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F A122255 a(n) = if A006530(A000010(n)) <= 3 then 1 else 0.
%F A122255 a(A122254(n)) = a(A048135(n)) = 1; a(A048136(n)) = 0.
%F A122255 a(n) = if n=1 then 0 else A122256(n) - A122256(n-1).
%F A122255 a(n) = A122261(n) for n < 25.
%F A122255 a(n) = A065333(A000010(n)). - _Antti Karttunen_, Aug 22 2017
%F A122255 Multiplicative with a(p^e) = 1 for e = 1 and A006530(p-1) <= 3 or p <= 3; otherwise 0. - _Andrew Howroyd_, Aug 01 2018
%e A122255 For n = 25, phi(25) = 20 = 2^2 * 5^1, and this is not 3-smooth, thus a(25) = 0.
%e A122255 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
%t A122255 a[n_] := Boole[FactorInteger[EulerPhi[n]][[-1, 1]] <= 3];
%t A122255 a /@ Range[1, 100] (* _Jean-François Alcover_, Sep 20 2019 *)
%o A122255 (PARI) a(n)=n=eulerphi(n); n>>=valuation(n, 2); n==3^valuation(n, 3) \\ _Charles R Greathouse IV_, Feb 21 2013
%Y A122255 Cf. A000010, A006530, A065333, A122261, A122256 (partial sums).
%Y A122255 Characteristic function of A122254.
%K A122255 nonn,mult
%O A122255 1,1
%A A122255 _Reinhard Zumkeller_, Aug 29 2006

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