cp's OEIS Frontend

A368922 a(n) = n' - n''*2, where n' is the arithmetic derivative of n, A003415(n) and n'' is the second arithmetic derivative, A068346(n).

%I A368922 #14 May 06 2025 11:28:15
%S A368922 0,0,1,1,-4,1,3,1,-20,-4,5,1,-48,1,-3,-16,-128,1,1,1,-64,-4,11,1,-52,
%T A368922 -4,-1,-27,-128,1,29,1,-272,-4,17,-20,-124,1,1,-48,-76,1,39,1,-176,7,
%U A368922 5,1,-368,-4,-33,-28,-128,1,-135,-48,-100,-4,29,1,-100,1,5,11,-1088,-24,59,1,-240,-4,57,1,-284,1,7,23,-272
%N A368922 a(n) = n' - n''*2, where n' is the arithmetic derivative of n, A003415(n) and n'' is the second arithmetic derivative, A068346(n).
%H A368922 Antti Karttunen, <a href="/A368922/b368922.txt">Table of n, a(n) for n = 0..16384</a>
%F A368922 a(n) = A003415(n) - 2*A068346(n).
%F A368922 a(n) = A368921(n) - A068346(n).
%o A368922 (PARI)
%o A368922 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A368922 A368922(n) = { my(u=A003415(n)); (u-2*A003415(u)); };
%Y A368922 Cf. A003415, A068346, A334261 (positions of -4's), A368701, A368921.
%K A368922 sign
%O A368922 0,5
%A A368922 _Antti Karttunen_, Jan 10 2024