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A351233 a(n) = A276085(A351231(n)).

%I A351233 #12 Feb 05 2022 17:05:16
%S A351233 0,0,2,3,4,5,0,7,6,6,10,11,12,13,12,14,16,17,18,19,18,14,22,23,24,18,
%T A351233 18,25,28,29,30,31,32,2,34,32,30,37,6,38,40,41,42,43,42,43,34,47,18,
%U A351233 18,42,44,22,53,54,54,56,56,58,59,60,61,60,61,62,60,66,67,66,68,70,71,72,73,72,69,70,72,78,79,80,78
%N A351233 a(n) = A276085(A351231(n)).
%H A351233 Antti Karttunen, <a href="/A351233/b351233.txt">Table of n, a(n) for n = 0..65537</a>
%H A351233 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A351233 a(n) = A276085(A351231(n)) = A276085(A276086(n) / gcd(A003415(n), A276086(n))).
%F A351233 a(n) = n - A351234(n).
%o A351233 (PARI)
%o A351233 A002110(n) = prod(i=1,n,prime(i));
%o A351233 A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
%o A351233 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A351233 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A351233 A351231(n) = { my(u=A276086(n)); u/gcd(A003415(n), u); };
%o A351233 A351233(n) = A276085(A351231(n));
%Y A351233 Cf. A003415, A276085, A276086, A351231, A351234.
%K A351233 nonn,base,easy,look
%O A351233 0,3
%A A351233 _Antti Karttunen_, Feb 05 2022