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A342016 Difference between the arithmetic derivative of A276086(n) and A276086(n) itself, which is the prime product form of primorial base expansion of n.

%I A342016 #15 Mar 14 2021 20:42:33
%S A342016 -1,-1,-2,-1,-3,3,-4,-3,-7,1,-6,33,-15,-5,-20,35,15,255,-50,25,-25,
%T A342016 325,300,1725,-125,375,250,2375,2625,10875,-6,-5,-11,-1,-12,39,-23,
%U A342016 -11,-34,37,3,321,-80,15,-65,395,330,2235,-225,425,200,3025,3225,14325,-250,3875,3625,20375,24000,87375,-35,-21,-56,35,-21
%N A342016 Difference between the arithmetic derivative of A276086(n) and A276086(n) itself, which is the prime product form of primorial base expansion of n.
%H A342016 Antti Karttunen, <a href="/A342016/b342016.txt">Table of n, a(n) for n = 0..2310</a>
%H A342016 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A342016 a(n) = A168036(A276086(n)) = A327860(n) - A276086(n).
%F A342016 For all n >= 0, gcd(a(n), A276086(n)) = gcd(a(n), A327860(n)) = A328572(n).
%o A342016 (PARI)
%o A342016 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A342016 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A342016 A327860(n) = A003415(A276086(n));
%o A342016 A342016(n) = (A327860(n) - A276086(n));
%Y A342016 Cf. A003415, A168036, A276086, A327860, A328572, A342002, A342015, A342026.
%K A342016 sign,look
%O A342016 0,3
%A A342016 _Antti Karttunen_, Mar 04 2021