A343220 Number of unitary divisors d of n for which A003415(sigma(d)) > d.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Apr 09 2021

Keywords

• nonn
• look

Comments

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

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

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

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A343219(n) = (A003415(sigma(n))>n);
A343220(n) = sumdiv(n,d,if(1==gcd(d,n/d),A343219(d),0));

Formula

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