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A353575 Primepi based arithmetic derivative applied to the prime shadow of the primorial base exp-function: a(n) = A258851(A181819(A276086(n))).

%I A353575 #15 Apr 30 2022 22:51:25
%S A353575 0,1,1,4,2,7,1,4,4,12,7,20,2,7,7,20,12,33,3,11,11,32,19,53,4,15,15,44,
%T A353575 26,73,1,4,4,12,7,20,4,12,12,32,20,52,7,20,20,52,33,84,11,32,32,84,53,
%U A353575 136,15,44,44,116,73,188,2,7,7,20,12,33,7,20,20,52,33,84,12,33,33,84,54,135,19,53,53,136,87,219
%N A353575 Primepi based arithmetic derivative applied to the prime shadow of the primorial base exp-function: a(n) = A258851(A181819(A276086(n))).
%H A353575 Antti Karttunen, <a href="/A353575/b353575.txt">Table of n, a(n) for n = 0..11550</a>
%H A353575 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A353575 a(n) = A353379(A276086(n)) = A258851(A328835(n)).
%o A353575 (PARI)
%o A353575 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A353575 A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
%o A353575 A258851(n) = (n*sum(i=1, #n=factor(n)~, n[2, i]*primepi(n[1, i])/n[1, i])); \\ From A258851
%o A353575 A353379(n) = A258851(A181819(n));
%o A353575 A353575(n) = A353379(A276086(n));
%Y A353575 Cf. A181819, A258851, A276086, A328835, A353379.
%Y A353575 Cf. also A342002, A353574 and A353576.
%K A353575 nonn,base,easy,look
%O A353575 0,4
%A A353575 _Antti Karttunen_, Apr 29 2022