cp's OEIS Frontend

A368921 a(n) = n' - n'', where n' is the arithmetic derivative of n, A003415(n) and n'' is its second arithmetic derivative, A068346(n).

%I A368921 #9 May 06 2025 11:28:05
%S A368921 0,0,1,1,0,1,4,1,-4,1,6,1,-16,1,3,-4,-48,1,11,1,-20,3,12,1,-4,3,7,0,
%T A368921 -48,1,30,1,-96,5,18,-4,-32,1,11,-16,-4,1,40,1,-64,23,15,1,-128,5,6,
%U A368921 -4,-36,1,-27,-16,-4,9,30,1,-4,1,19,31,-448,-3,60,1,-84,11,58,1,-64,1,23,39,-96,-3,70,1,-192,-108,42
%N A368921 a(n) = n' - n'', where n' is the arithmetic derivative of n, A003415(n) and n'' is its second arithmetic derivative, A068346(n).
%H A368921 Antti Karttunen, <a href="/A368921/b368921.txt">Table of n, a(n) for n = 0..16384</a>
%F A368921 a(n) = A003415(n) - A068346(n).
%F A368921 a(n) = A368922(n) + A068346(n).
%o A368921 (PARI)
%o A368921 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A368921 A368921(n) = { my(u=A003415(n)); (u-A003415(u)); };
%Y A368921 Cf. A003415, A068346, A348329 (positions of 0's), A368922.
%K A368921 sign
%O A368921 0,7
%A A368921 _Antti Karttunen_, Jan 10 2024