cp's OEIS Frontend

A355003 a(n) = gcd(A003415(n), A277791(n)), where A003415 is the arithmetic derivative and A277791 is the denominator of sum of reciprocals of proper divisors of n.

%I A355003 #8 Jul 18 2022 16:38:49
%S A355003 1,1,1,2,1,1,1,4,3,1,1,4,1,1,1,8,1,3,1,4,1,1,1,4,5,1,9,4,1,1,1,16,1,1,
%T A355003 1,2,1,1,1,4,1,1,1,4,3,1,1,16,7,5,1,4,1,27,1,4,1,1,1,4,1,1,3,32,1,1,1,
%U A355003 4,1,1,1,12,1,1,5,4,1,1,1,16,27,1,1,4,1,1,1,4,1,3,1,4,1,1,1,16,1,7,3,5,1,1,1,4,1
%N A355003 a(n) = gcd(A003415(n), A277791(n)), where A003415 is the arithmetic derivative and A277791 is the denominator of sum of reciprocals of proper divisors of n.
%H A355003 Antti Karttunen, <a href="/A355003/b355003.txt">Table of n, a(n) for n = 1..65537</a>
%F A355003 a(n) = gcd(A003415(n), A277791(n)).
%F A355003 a(p^k) = p^(k-1) for all primes p and exponents k > 0.
%o A355003 (PARI)
%o A355003 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A355003 A277791(n) = denominator((sigma(n)-1)/n); \\ From A277791
%o A355003 A355003(n) = gcd(A003415(n), A277791(n));
%Y A355003 Cf. A003415, A277791.
%Y A355003 Cf. also A355815.
%K A355003 nonn
%O A355003 1,4
%A A355003 _Antti Karttunen_, Jul 18 2022