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A354099 The 3-adic valuation of Euler totient function phi.

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%I A354099 #14 May 18 2022 10:07:17
%S A354099 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,
%T A354099 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,
%U A354099 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
%N A354099 The 3-adic valuation of Euler totient function phi.
%H A354099 Antti Karttunen, <a href="/A354099/b354099.txt">Table of n, a(n) for n = 1..65537</a>
%F A354099 a(n) = A007949(A000010(n)).
%F A354099 Additive with a(p^e) = A007949((p-1)*p^(e-1)).
%t A354099 a[n_] := IntegerExponent[EulerPhi[n], 3]; Array[a, 100] (* _Amiram Eldar_, May 17 2022 *)
%o A354099 (PARI) A354099(n) = valuation(eulerphi(n),3);
%o A354099 (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.
%Y A354099 Cf. A000010, A007949, A074942.
%Y A354099 Cf. A088232 (positions of zeros), A066498 (of terms > 0).
%Y A354099 Cf. also A354100.
%K A354099 nonn
%O A354099 1,19
%A A354099 _Antti Karttunen_, May 17 2022