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
Examples
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
Links
Crossrefs
Programs
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Mathematica
a[n_] := Boole[FactorInteger[EulerPhi[n]][[-1, 1]] <= 3]; a /@ Range[1, 100] (* Jean-François Alcover, Sep 20 2019 *)
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PARI
a(n)=n=eulerphi(n); n>>=valuation(n, 2); n==3^valuation(n, 3) \\ Charles R Greathouse IV, Feb 21 2013
Formula
a(n) = A122261(n) for n < 25.
Multiplicative with a(p^e) = 1 for e = 1 and A006530(p-1) <= 3 or p <= 3; otherwise 0. - Andrew Howroyd, Aug 01 2018
Comments