cp's OEIS Frontend

A345000 a(n) = gcd(A003415(n), A003415(A276086(n))), where A003415(n) is the arithmetic derivative of n, and A276086(n) gives the prime product form of primorial base expansion of n.

%I A345000 #16 May 03 2022 08:20:43
%S A345000 0,1,1,1,2,1,1,1,4,1,1,1,2,1,1,1,16,1,3,1,2,5,1,1,4,5,5,1,2,1,1,1,10,
%T A345000 1,1,3,12,1,1,1,2,1,1,1,4,1,5,1,2,1,5,5,4,1,3,1,2,1,1,1,2,1,1,1,12,3,
%U A345000 1,1,2,1,1,1,12,1,1,55,10,3,1,1,16,1,1,1,2,1,5,1,140,1,3,1,16,1,49,3,2,1,7,1,28,1,7,1,2,1
%N A345000 a(n) = gcd(A003415(n), A003415(A276086(n))), where A003415(n) is the arithmetic derivative of n, and A276086(n) gives the prime product form of primorial base expansion of n.
%H A345000 Antti Karttunen, <a href="/A345000/b345000.txt">Table of n, a(n) for n = 0..65537</a>
%H A345000 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A345000 a(n) = gcd(A003415(n), A327860(n)) = gcd(A003415(n), A003415(A276086(n))).
%o A345000 (PARI)
%o A345000 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A345000 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A345000 A345000(n) = gcd(A003415(n), A003415(A276086(n)));
%Y A345000 Cf. A003415, A276086, A327860, A347958 (inverse Möbius transform), A347959, A351083, A351085, A351086, A351235, A351236.
%Y A345000 Cf. A166486 (a(n) mod 2, parity of terms, see comment in A327860).
%Y A345000 Cf. also A324198, A327858.
%K A345000 nonn,base,easy,look
%O A345000 0,5
%A A345000 _Antti Karttunen_, Jul 21 2021