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A369049 a(n) = n mod n', where n' is the arithmetic derivative of n, A003415.

%I A369049 #9 Jan 15 2024 14:44:30
%S A369049 0,0,0,0,1,0,8,3,3,0,12,0,5,7,16,0,18,0,20,1,9,0,24,5,11,0,28,0,30,0,
%T A369049 32,5,15,11,36,0,17,7,40,0,1,0,44,6,21,0,48,7,5,11,52,0,54,7,56,13,27,
%U A369049 0,60,0,29,12,64,11,5,0,68,17,11,0,72,0,35,20,76,5,7,0,80,81,39,0,84,19,41,23,88,0,90,11
%N A369049 a(n) = n mod n', where n' is the arithmetic derivative of n, A003415.
%H A369049 Antti Karttunen, <a href="/A369049/b369049.txt">Table of n, a(n) for n = 2..65537</a>
%F A369049 a(n) = n mod A003415(n).
%t A369049 Array[Mod[#, #  Total[#2/#1 & @@@ FactorInteger[#]]] &, 120, 2] (* _Michael De Vlieger_, Jan 15 2024 *)
%o A369049 (PARI)
%o A369049 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A369049 A369049(n) = (n % A003415(n));
%Y A369049 Cf. A003415, A085731 [= gcd(A003415(n), a(n))].
%Y A369049 Cf. also A328382, A342014, A369050.
%K A369049 nonn
%O A369049 2,7
%A A369049 _Antti Karttunen_, Jan 15 2024