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A328320 Numbers for which A328311(n) = 1 + A051903(A003415(n)) - A051903(n) is zero (including 1 as the initial term).

%I A328320 #9 Oct 13 2019 18:09:15
%S A328320 1,2,3,5,7,8,9,11,13,17,18,19,23,24,25,29,31,32,37,40,41,43,45,47,49,
%T A328320 53,56,59,61,63,67,71,72,73,75,79,81,83,88,89,90,96,97,98,101,103,104,
%U A328320 107,109,113,117,120,121,125,126,127,128,131,136,137,139,147,149,150,151,152,153,157,160,162,163,167,168,169
%N A328320 Numbers for which A328311(n) = 1 + A051903(A003415(n)) - A051903(n) is zero (including 1 as the initial term).
%C A328320 After 1, the numbers whose "degree" (maximal exponent, A051903) is decremented by one when arithmetic derivative (A003415) is applied to them.
%H A328320 Antti Karttunen, <a href="/A328320/b328320.txt">Table of n, a(n) for n = 1..20000</a>
%o A328320 (PARI)
%o A328320 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A328320 A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
%o A328320 A328311(n) = if(n<=1,0,1+(A051903(A003415(n)) - A051903(n)));
%o A328320 isA328320(n) = (0==A328311(n));
%Y A328320 Cf. A003415, A051903, A328302, A328310.
%Y A328320 Indices of zeros in A328311.
%Y A328320 Cf. A328321 (complement), A328252 (a subsequence).
%K A328320 nonn
%O A328320 1,2
%A A328320 _Antti Karttunen_, Oct 13 2019