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A369971 a(n) = A003415(n) mod A276086(n), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

%I A369971 #8 Feb 07 2024 14:53:18
%S A369971 0,0,1,1,4,1,0,1,12,6,7,1,16,1,9,8,32,1,21,1,24,10,13,1,44,10,15,27,
%T A369971 32,1,3,1,17,14,19,12,25,1,21,16,68,1,41,1,48,39,25,1,112,14,45,20,56,
%U A369971 1,81,16,92,22,31,1,43,1,33,51,192,18,61,1,72,26,59,1,156,1,39,55,80,18,71,1,176,108,43,1,124,22
%N A369971 a(n) = A003415(n) mod A276086(n), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
%H A369971 Antti Karttunen, <a href="/A369971/b369971.txt">Table of n, a(n) for n = 0..65537</a>
%H A369971 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A369971 (PARI)
%o A369971 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A369971 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A369971 A369971(n) = (A003415(n)%A276086(n));
%Y A369971 Cf. A003415, A276086, A369970 (positions of 0's).
%Y A369971 Cf. also A327858 [= gcd(a(n), A276086(n))], A328382, A342014.
%K A369971 nonn
%O A369971 0,5
%A A369971 _Antti Karttunen_, Feb 07 2024