A387725 Number of unitary divisors d of n for which A107758(d) > 2*d, where A107758 is sigma+, multiplicative function with a(p^e) = 1+sigma(p^e).

0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 4, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 4, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 4, 0, 1, 0, 0, 0, 3, 0, 1, 0, 3, 0, 1, 0, 1, 1, 1, 0, 3, 0, 1, 0, 1, 0, 4, 0, 1, 0, 1, 0, 4, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 3, 0, 1, 3

Offset: 1

Author

Antti Karttunen, Sep 06 2025

Keywords

• nonn
• new

Links

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

Crossrefs

Cf. A107758, A387721 (positions of positive terms).

Cf. also A387715, A337345.

Programs

PARI

A107758(n) =  { my(f = factor(n)); prod(k=1, #f~, 1+sigma(f[k, 1]^f[k, 2])); };
A387725(n) = sumdiv(n,d,(1==gcd(d,n/d)) && (A107758(d)>(2*d)));

Formula

a(n) = Sum_{d|n} [gcd(d,n/d)==1 and A107758(d) > 2*d], where [ ] is the Iverson bracket.