A342003 - OEIS

%I #13 Mar 07 2021 19:06:41

%S 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 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 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 Maximal exponent in the prime factorization of the arithmetic derivative of n: a(n) = A051903(A003415(n)).

%H Antti Karttunen, <a href="/A342003/b342003.txt">Table of n, a(n) for n = 2..65537</a>

%F a(n) = A051903(A003415(n)).

%F a(n) = A051903(n) + A328310(n).

%F a(n) = 1 iff A341994(n) = 1.

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));

%o A342003(n) = A051903(A003415(n));

%Y Cf. A003415, A051903, A328310, A328311, A328320, A328321, A341994, A341995, A342004.

%Y Cf. A000040 (indices of zeros), A328234 (of ones), A328393 (of the terms < 2).

%K nonn

%O 2,3

%A _Antti Karttunen_, Mar 01 2021