cp's OEIS Frontend

A351234 a(n) = A276085(gcd(A003415(n), A276086(n))).

%I A351234 #13 Dec 25 2024 02:02:34
%S A351234 0,1,0,0,0,0,6,0,2,3,0,0,0,0,2,1,0,0,0,0,2,7,0,0,0,7,8,2,0,0,0,0,0,31,
%T A351234 0,3,6,0,32,1,0,0,0,0,2,2,12,0,30,31,8,7,30,0,0,1,0,1,0,0,0,0,2,2,2,5,
%U A351234 0,0,2,1,0,0,0,0,2,6,6,5,0,0,0,3,0,0,0,1,8,1,36,0,0,1,2,1,60,3,0,0,30,8,36,0,30
%N A351234 a(n) = A276085(gcd(A003415(n), A276086(n))).
%H A351234 Antti Karttunen, <a href="/A351234/b351234.txt">Table of n, a(n) for n = 0..11550</a>
%H A351234 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A351234 a(n) = A276085(A327858(n)) = A276085(gcd(A003415(n), A276086(n))).
%F A351234 a(n) = n - A351233(n).
%o A351234 (PARI)
%o A351234 A002110(n) = prod(i=1,n,prime(i));
%o A351234 A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
%o A351234 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A351234 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A351234 A327858(n) = gcd(A003415(n), A276086(n));
%o A351234 A351234(n) = A276085(A327858(n));
%Y A351234 Cf. A003415, A276085, A276086, A327858, A351233.
%Y A351234 Cf. also A351254.
%K A351234 nonn,base,easy
%O A351234 0,7
%A A351234 _Antti Karttunen_, Feb 05 2022