A348494 - OEIS

%I #19 Nov 13 2021 22:33:53

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

%H Antti Karttunen, <a href="/A348494/b348494.txt">Table of n, a(n) for n = 1..10000</a>

%H Antti Karttunen, <a href="/A348494/a348494.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%F a(n) = gcd(A342001(n), A347128(n)).

%F a(n) = A348492(n) / A003557(n), where A348492(n) = gcd(A003415(n), A018804(n)).

%t 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 (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A003557(n) = (n/factorback(factorint(n)[, 1]));

%o A018804(n) = sumdiv(n, d, n*eulerphi(d)/d); \\ From A018804

%o A348492(n) = gcd(A003415(n), A018804(n));

%o A348494(n) = (A348492(n)/A003557(n));

%Y Cf. A003415, A003557, A018804, A342001, A347128, A348492, A348500 [= a(A276086(n))].

%Y Cf. also A348496.

%K nonn

%O 1,4

%A _Antti Karttunen_, Oct 21 2021