A381136 a(n) is the number of divisors d of n such that tau(d^(1 + n) + n) = 2^omega(d^(1 + n) + n), where tau = A000005 and omega = A001221.

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

Offset: 1

Author

Juri-Stepan Gerasimov, Feb 15 2025

Keywords

• nonn

Crossrefs

Cf. A000005, A001221, A049533, A381138.

Programs

Magma

[#[d: d in Divisors(n) | #Divisors(d^(1+n)+n) eq 2^#PrimeDivisors(d^(1+n)+n)]: n in [1..50]];

Mathematica

Table[Length[Select[Divisors[n],DivisorSigma[0,#^(1+n)+n]==2^PrimeNu[#^(1+n)+n]&]],{n,45}] (* James C. McMahon, Mar 05 2025 *)

PARI

a(n) = sumdiv(n, d, my(f=factor(d^(1 + n) + n)); numdiv(f) == 2^omega(f)); \\ Michel Marcus, Feb 15 2025

Extensions

More terms from Jinyuan Wang, Mar 09 2025