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A366801 Arithmetic derivative without its inherited divisor applied to the Doudna sequence: a(n) = A342001(A005940(1+n)).

%I A366801 #11 Oct 24 2023 12:21:19
%S A366801 0,1,1,2,1,5,2,3,1,7,8,8,2,7,3,4,1,9,10,12,12,31,13,11,2,9,11,10,3,9,
%T A366801 4,5,1,13,14,16,16,41,17,17,18,59,71,46,19,41,18,14,2,11,13,14,17,37,
%U A366801 16,13,3,11,14,12,4,11,5,6,1,15,16,24,18,61,25,23,20,87,103,62,27,55,24,22,24,113,131,94,167,247
%N A366801 Arithmetic derivative without its inherited divisor applied to the Doudna sequence: a(n) = A342001(A005940(1+n)).
%H A366801 Antti Karttunen, <a href="/A366801/b366801.txt">Table of n, a(n) for n = 0..16384</a>
%o A366801 (PARI)
%o A366801 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A366801 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A366801 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A366801 A342001(n) = (A003415(n) / A003557(n));
%o A366801 A366801(n) = A342001(A005940(1+n));
%Y A366801 Cf. A003415, A005940, A342001, A344026, A366802 (rgs-transform).
%Y A366801 Cf. also A342002.
%K A366801 nonn,look
%O A366801 0,4
%A A366801 _Antti Karttunen_, Oct 24 2023