A381733 Number of divisors d of n such that 2^omega(n + d) = tau(n + d), where omega = A001221 and tau = A000005.

1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 3, 2, 2, 1, 1, 1, 2, 1, 3, 2, 2, 1, 2, 2, 1, 1, 4, 2, 3, 1, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 1, 1, 3, 1, 2, 1, 1, 0, 2, 1, 3, 1, 2, 2, 3, 2, 2, 1, 5, 2, 1, 2, 2, 4, 3, 1, 4, 2, 3, 1, 3, 2, 1, 1, 4, 2, 2, 1, 2, 1, 2, 1, 5, 3, 2, 1, 2, 1, 4, 1, 4, 2, 2, 2, 2, 1, 1, 2, 4

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 05 2025

Keywords

• nonn

Crossrefs

Cf. A000005, A001221, A005117, A381136, A381138.

Programs

Magma

[#[d: d in Divisors(n) | 2^#PrimeDivisors(n+d) eq #Divisors(n+d)]: n in [1..100]];

Mathematica

a[n_]:=Length[Select[Divisors[n], DivisorSigma[0, #+n]==2^PrimeNu[#+n]&]]; Array[a,100] (* Stefano Spezia, Mar 07 2025 *)