cp's OEIS Frontend

A348492 Greatest common divisor of the arithmetic derivative (A003415) and Pillai's arithmetical function (A018804).

%I A348492 #13 Feb 02 2022 20:36:12
%S A348492 1,1,1,4,1,5,1,4,3,1,1,8,1,3,1,16,1,21,1,24,5,1,1,4,5,15,27,8,1,1,1,
%T A348492 16,7,1,3,12,1,3,1,4,1,1,1,24,3,5,1,16,7,15,5,8,1,81,1,4,1,1,1,4,1,3,
%U A348492 3,64,9,1,1,24,1,1,1,12,1,3,5,8,3,1,1,16,27,1,1,4,11,15,1,140,1,3,5,24,1,1,3,16,1,7
%N A348492 Greatest common divisor of the arithmetic derivative (A003415) and Pillai's arithmetical function (A018804).
%H A348492 Antti Karttunen, <a href="/A348492/b348492.txt">Table of n, a(n) for n = 1..20000</a>
%F A348492 a(n) = gcd(A003415(n), A018804(n)).
%F A348492 For n > 1, a(n) = A003415(n) / A348493(n).
%F A348492 a(n) = A003557(n) * A348494(n).
%t A348492 Array[GCD[Total@ GCD[#, Range[#]], # Total[#2/#1 & @@@ FactorInteger[#]]] &, 98] (* _Michael De Vlieger_, Oct 21 2021 *)
%o A348492 (PARI)
%o A348492 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A348492 A018804(n) = sumdiv(n, d, n*eulerphi(d)/d); \\ From A018804
%o A348492 A348492(n) = gcd(A003415(n), A018804(n));
%Y A348492 Cf. A003415, A003557, A018804, A348493, A348494.
%Y A348492 Cf. also A342413, A342458, A348495.
%K A348492 nonn
%O A348492 1,4
%A A348492 _Antti Karttunen_, Oct 21 2021