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%I A342003 #13 Mar 07 2021 19:06:41
%S A342003 0,0,2,0,1,0,2,1,1,0,4,0,2,3,5,0,1,0,3,1,1,0,2,1,1,3,5,0,1,0,4,1,1,2,
%T A342003 2,0,1,4,2,0,1,0,4,1,2,0,4,1,2,2,3,0,4,4,2,1,1,0,2,0,1,1,6,2,1,0,3,1,
%U A342003 1,0,2,0,1,1,4,2,1,0,4,3,1,0,2,1,2,5,2,0,1,2,5,1,2,3,4,0,1,2,2,0,1,0,2,1
%N A342003 Maximal exponent in the prime factorization of the arithmetic derivative of n: a(n) = A051903(A003415(n)).
%H A342003 Antti Karttunen, <a href="/A342003/b342003.txt">Table of n, a(n) for n = 2..65537</a>
%F A342003 a(n) = A051903(A003415(n)).
%F A342003 a(n) = A051903(n) + A328310(n).
%F A342003 a(n) = 1 iff A341994(n) = 1.
%o A342003 (PARI)
%o A342003 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A342003 A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
%o A342003 A342003(n) = A051903(A003415(n));
%Y A342003 Cf. A003415, A051903, A328310, A328311, A328320, A328321, A341994, A341995, A342004.
%Y A342003 Cf. A000040 (indices of zeros), A328234 (of ones), A328393 (of the terms < 2).
%K A342003 nonn
%O A342003 2,3
%A A342003 _Antti Karttunen_, Mar 01 2021

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