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A348493 a(n) = A003415(n) / gcd(A003415(n), A018804(n)), where A003415 is the arithmetic derivative and A018804 is Pillai's arithmetical function.

%I A348493 #13 Feb 02 2022 20:36:17
%S A348493 0,1,1,1,1,1,1,3,2,7,1,2,1,3,8,2,1,1,1,1,2,13,1,11,2,1,1,4,1,31,1,5,2,
%T A348493 19,4,5,1,7,16,17,1,41,1,2,13,5,1,7,2,3,4,7,1,1,16,23,22,31,1,23,1,11,
%U A348493 17,3,2,61,1,3,26,59,1,13,1,13,11,10,6,71,1,11,4,43,1,31,2,3,32,1,1,41,4,4,34,49,8
%N A348493 a(n) = A003415(n) / gcd(A003415(n), A018804(n)), where A003415 is the arithmetic derivative and A018804 is Pillai's arithmetical function.
%H A348493 Antti Karttunen, <a href="/A348493/b348493.txt">Table of n, a(n) for n = 1..20000</a>
%F A348493 a(n) = A003415(n) / A348492(n).
%t A348493 Array[#2/GCD[#1, #2] & @@ {Total@ GCD[#, Range[#]], If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]]} &, 95] (* _Michael De Vlieger_, Oct 21 2021 *)
%o A348493 (PARI)
%o A348493 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A348493 A018804(n) = sumdiv(n, d, n*eulerphi(d)/d); \\ From A018804
%o A348493 A348493(n) = { my(u=A003415(n)); (u/gcd(u,A018804(n))); };
%Y A348493 Cf. A003415, A018804, A348492, A348494.
%K A348493 nonn
%O A348493 1,8
%A A348493 _Antti Karttunen_, Oct 21 2021