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%I #13 Feb 02 2022 20:36:22
%S 1,1,1,2,1,5,1,4,3,1,1,8,1,3,1,16,1,63,1,72,5,1,1,4,5,15,27,8,1,1,1,
%T 16,7,1,3,6,1,3,1,4,1,1,1,24,9,5,1,80,7,15,5,8,1,81,1,4,1,1,1,24,1,3,
%U 3,32,9,1,1,24,1,1,1,12,1,3,5,8,3,1,1,16,27,1,1,8,11,15,1,140,1,9,5,72,1,1,3,16,1
%N a(n) = gcd(A018804(n), A347130(n)), where A347130 is the Dirichlet convolution of the identity function with the arithmetic derivative of n (A003415), and A018804 is Pillai's arithmetical function.
%H Antti Karttunen, <a href="/A348495/b348495.txt">Table of n, a(n) for n = 1..20000</a>
%F a(n) = gcd(A018804(n), A347130(n)).
%F a(n) = A003557(n) * A348496(n).
%t Table[GCD[Total@ GCD[n, Range[n]], DivisorSum[n, #*(If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &[n/#]) &]], {n, 97}] (* _Michael De Vlieger_, Oct 21 2021 *)
%o (PARI)
%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A018804(n) = sumdiv(n, d, n*eulerphi(d)/d); \\ From A018804
%o A347130(n) = sumdiv(n,d,d*A003415(n/d));
%o A348495(n) = gcd(A018804(n), A347130(n));
%Y Cf. A003415, A003557, A018804, A347130, A348496.
%Y Cf. also A348492, A348497.
%K nonn
%O 1,4
%A _Antti Karttunen_, Oct 21 2021
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