A387715 Number of divisors d of n for which A003959(d) > 2*d, where A003959 is multiplicative with a(p^e) = (p+1)^e.

0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 3, 0, 1, 0, 2, 0, 0, 0, 4, 0, 0, 1, 2, 0, 1, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 1, 0, 2, 1, 0, 0, 6, 0, 1, 0, 2, 0, 3, 0, 4, 0, 0, 0, 5, 0, 0, 1, 5, 0, 1, 0, 2, 0, 1, 0, 7, 0, 0, 0, 2, 0, 1, 0, 6, 2, 0, 0, 5, 0, 0, 0, 4, 0, 4, 0, 2, 0, 0, 0, 8, 0, 0, 0, 4, 0, 1, 0, 4, 0

Offset: 1

Author

Antti Karttunen, Sep 06 2025

Keywords

• nonn
• new

Comments

Number of terms of A387711 that divide n.

Links

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

Crossrefs

Cf. A003959, A387711 (positions of terms > 0), A387712 (of 1's), A387713 (of terms > 1).

Cf. also A080224, A337345.

Programs

PARI

A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
is_A387711(n) = (A003959(n)>(2*n));
A387715(n) = sumdiv(n,d,is_A387711(d));

Formula

a(n) = Sum_{d|n} [A003959(d) > 2*d], where [ ] is the Iverson bracket.