cp's OEIS Frontend

A348494 a(n) = A348492(n) / A003557(n), where A348492 is the GCD of the arithmetic derivative (A003415) and Pillai's arithmetical function (A018804).

%I A348494 #19 Nov 13 2021 22:33:53
%S A348494 1,1,1,2,1,5,1,1,1,1,1,4,1,3,1,2,1,7,1,12,5,1,1,1,1,15,3,4,1,1,1,1,7,
%T A348494 1,3,2,1,3,1,1,1,1,1,12,1,5,1,2,1,3,5,4,1,9,1,1,1,1,1,2,1,3,1,2,9,1,1,
%U A348494 12,1,1,1,1,1,3,1,4,3,1,1,2,1,1,1,2,11,15,1,35,1,1,5,12,1,1,3,1,1,1,1,2,1,1,1,1,1
%N A348494 a(n) = A348492(n) / A003557(n), where A348492 is the GCD of the arithmetic derivative (A003415) and Pillai's arithmetical function (A018804).
%H A348494 Antti Karttunen, <a href="/A348494/b348494.txt">Table of n, a(n) for n = 1..10000</a>
%H A348494 Antti Karttunen, <a href="/A348494/a348494.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A348494 a(n) = gcd(A342001(n), A347128(n)).
%F A348494 a(n) = A348492(n) / A003557(n), where A348492(n) = gcd(A003415(n), A018804(n)).
%t A348494 Array[GCD[Total@ GCD[#1, Range[#1]], #1 Total[#2/#1 & @@@ #2]]/Apply[Times, Map[#1^(#2 - 1) & @@ # &, #2]] & @@ {#, FactorInteger[#]} &, 105] (* _Michael De Vlieger_, Oct 21 2021 *)
%o A348494 (PARI)
%o A348494 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A348494 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A348494 A018804(n) = sumdiv(n, d, n*eulerphi(d)/d); \\ From A018804
%o A348494 A348492(n) = gcd(A003415(n), A018804(n));
%o A348494 A348494(n) = (A348492(n)/A003557(n));
%Y A348494 Cf. A003415, A003557, A018804, A342001, A347128, A348492, A348500 [= a(A276086(n))].
%Y A348494 Cf. also A348496.
%K A348494 nonn
%O A348494 1,4
%A A348494 _Antti Karttunen_, Oct 21 2021