A369052 - OEIS

%I #9 Jan 17 2024 20:51:48

%S 0,1,0,1,-4,3,-4,5,-16,-3,-4,9,-20,11,-4,-1,-48,15,-24,17,-28,1,-4,21,

%T -64,5,-4,-27,-36,27,-32,29,-128,5,-4,11,-84,35,-4,7,-96,39,-40,41,

%U -52,-33,-4,45,-176,21,-40,11,-60,51,-108,23,-128,13,-4,57,-124,59,-4,-39,-320,29,-56,65,-76,17,-48,69,-240,71

%N a(n) = n - n'*2, where n' is the arithmetic derivative of n, A003415.

%H Antti Karttunen, <a href="/A369052/b369052.txt">Table of n, a(n) for n = 0..16384</a>

%F a(n) = n - 2*A003415(n).

%F a(n) = -(A003415(n)+A168036(n)).

%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 A369052(n) = (n-2*A003415(n));

%Y Cf. A003415.

%Y Cf. also A068719, A168036, A368921, A368922.

%K sign

%O 0,5

%A _Antti Karttunen_, Jan 17 2024