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A369669 The greatest common divisor of the first and the second arithmetic derivative of n.

%I A369669 #12 Feb 10 2024 18:52:24
%S A369669 0,0,1,1,4,1,1,1,4,1,1,1,16,1,3,4,16,1,1,1,4,1,1,1,4,1,1,27,16,1,1,1,
%T A369669 16,1,1,4,4,1,1,16,4,1,1,1,16,1,5,1,16,1,3,4,4,1,27,16,4,1,1,1,4,1,1,
%U A369669 1,64,3,1,1,12,1,1,1,4,1,1,1,16,3,1,1,16,108,1,1,4,1,3,16,4,1,1,4,16,1,7,4,16,1,1,5
%N A369669 The greatest common divisor of the first and the second arithmetic derivative of n.
%H A369669 Antti Karttunen, <a href="/A369669/b369669.txt">Table of n, a(n) for n = 0..16384</a>
%F A369669 a(n) = gcd(A003415(n), A068346(n)).
%F A369669 For n >= 2, a(n) = A085731(A003415(n)).
%o A369669 (PARI)
%o A369669 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A369669 A369669(n) = { my(d=A003415(n)); gcd(d, A003415(d)); };
%Y A369669 Cf. A003415, A068346, A085731, A370130 [= a(A276086(n))].
%Y A369669 Cf. A328393 (positions of 1's), A354874 (their characteristic function).
%Y A369669 Cf. A327864 (positions of even terms, also positions of multiples of 4).
%Y A369669 Cf. A370119 (positions of multiples of 3).
%K A369669 nonn
%O A369669 0,5
%A A369669 _Antti Karttunen_, Feb 10 2024