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

1,6

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

Formula

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

Prog

(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));

Crossrefs

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

Sequence in context: A335664 A269518 A219840 * A264893 A340653 A334744

Adjacent sequences: A343217 A343218 A343219 * A343221 A343222 A343223

Keyword

nonn,look

Author

Antti Karttunen, Apr 09 2021

Status

approved