A355003 - OEIS

%I #8 Jul 18 2022 16:38:49

%S 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 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 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 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 Antti Karttunen, <a href="/A355003/b355003.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = gcd(A003415(n), A277791(n)).

%F a(p^k) = p^(k-1) for all primes p and exponents k > 0.

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A277791(n) = denominator((sigma(n)-1)/n); \\ From A277791

%o A355003(n) = gcd(A003415(n), A277791(n));

%Y Cf. A003415, A277791.

%Y Cf. also A355815.

%K nonn

%O 1,4

%A _Antti Karttunen_, Jul 18 2022