A343220 - OEIS

%I #11 May 23 2021 03:20:32

%S 0,0,1,0,0,2,1,0,0,1,1,2,0,2,2,0,1,0,1,1,3,2,1,2,0,1,1,2,1,5,1,1,3,2,

%T 2,0,0,2,2,1,0,6,1,2,1,2,1,2,0,0,3,1,1,2,2,2,3,2,1,5,0,2,2,0,1,6,1,2,

%U 3,5,1,1,0,1,2,2,3,5,1,1,0,1,1,6,2,2,3,2,1,3,2,2,3,2,2,3,0,1,2,0,0,6,1,1,6

%N Number of unitary divisors d of n for which A003415(sigma(d)) > d.

%C Number of divisors d of n such that gcd(d,n/d) = 1 and d is in A343218.

%C Number of terms k of A343218 that divide n, and k and n/k are relatively prime.

%H Antti Karttunen, <a href="/A343220/b343220.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = Sum_{d|n, gcd(d,n/d)=1} A343219(d).

%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 A343219(n) = (A003415(sigma(n))>n);

%o A343220(n) = sumdiv(n,d,if(1==gcd(d,n/d),A343219(d),0));

%Y Cf. A000203, A003415, A342925, A343218, A343219, A343225 (positions of 1's).

%K nonn,look

%O 1,6

%A _Antti Karttunen_, Apr 09 2021