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A342014 Arithmetic derivative of n, taken modulo n: a(n) = A003415(n) mod n.

%I A342014 #11 Mar 14 2021 20:42:17
%S A342014 0,1,1,0,1,5,1,4,6,7,1,4,1,9,8,0,1,3,1,4,10,13,1,20,10,15,0,4,1,1,1,
%T A342014 16,14,19,12,24,1,21,16,28,1,41,1,4,39,25,1,16,14,45,20,4,1,27,16,36,
%U A342014 22,31,1,32,1,33,51,0,18,61,1,4,26,59,1,12,1,39,55,4,18,71,1,16,27,43,1,40,22,45,32,52,1,33
%N A342014 Arithmetic derivative of n, taken modulo n: a(n) = A003415(n) mod n.
%H A342014 Antti Karttunen, <a href="/A342014/b342014.txt">Table of n, a(n) for n = 1..16384</a>
%H A342014 Antti Karttunen, <a href="/A342014/a342014.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A342014 a(n) = A003415(n) mod n.
%o A342014 (PARI)
%o A342014 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A342014 A342014(n) = (A003415(n)%n);
%Y A342014 Cf. A003415, A072873 (positions of zeros), A085731 [= gcd(n, a(n))], A342015 [= A342014(A276086(n))].
%K A342014 nonn
%O A342014 1,6
%A A342014 _Antti Karttunen_, Mar 04 2021