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A373146 a(n) = A276085(n) - A003415(n), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

%I A373146 #6 May 26 2024 21:41:54
%S A373146 0,0,1,-2,5,-2,29,-9,-2,0,209,-12,2309,22,0,-28,30029,-16,510509,-16,
%T A373146 22,198,9699689,-39,2,2296,-21,0,223092869,-22,6469693229,-75,198,
%U A373146 30012,24,-54,200560490129,510490,2296,-59,7420738134809,-8,304250263527209,164,-29,9699666,13082761331670029,-106,46,-32,30012,2256
%N A373146 a(n) = A276085(n) - A003415(n), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.
%H A373146 Antti Karttunen, <a href="/A373146/b373146.txt">Table of n, a(n) for n = 1..2048</a>
%o A373146 (PARI)
%o A373146 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A373146 A002110(n) = prod(i=1,n,prime(i));
%o A373146 A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
%o A373146 A373146(n) = (A276085(n) - A003415(n));
%Y A373146 Cf. A003415, A276085, A369650 (positions of 0's), A373145.
%K A373146 sign
%O A373146 1,4
%A A373146 _Antti Karttunen_, May 26 2024