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A328382 a(n) = A276086(n) mod A003415(n), where A276086 is the primorial base exp-function and A003415 is the arithmetic derivative.

%I A328382 #19 Nov 26 2022 08:58:15
%S A328382 0,0,1,0,0,0,3,0,3,0,9,0,3,6,1,0,20,0,15,0,7,0,9,0,0,24,25,0,7,0,21,0,
%T A328382 6,6,35,0,0,2,43,0,11,0,45,36,0,0,91,0,15,10,35,0,1,14,61,4,5,0,49,0,
%U A328382 15,39,57,0,1,0,15,14,22,0,133,0,9,35,65,0,19,0,71,30,42,0,121,2,30,6,105,0,97,6,69,18,0,6,83,0,63,15,35,0,21
%N A328382 a(n) = A276086(n) mod A003415(n), where A276086 is the primorial base exp-function and A003415 is the arithmetic derivative.
%H A328382 Antti Karttunen, <a href="/A328382/b328382.txt">Table of n, a(n) for n = 2..30030</a>
%H A328382 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A328382 a(n) = A276086(n) mod A003415(n).
%F A328382 For n >= 2, gcd(a(n), A003415(n)) = A327858(n).
%o A328382 (PARI)
%o A328382 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A328382 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328382 A328382(n) = (A276086(n)%A003415(n));
%Y A328382 Cf. A003415, A276086, A327858, A358220, A358221 (positions of 0's), A358232 (of 1's), A358228 (of odd terms), A358229 (of even terms), A358227 (parity of terms).
%Y A328382 Cf. also A328386.
%K A328382 nonn
%O A328382 2,7
%A A328382 _Antti Karttunen_, Oct 15 2019