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

1,4

Links

Table of n, a(n) for n=1..100.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A384099 A138385 A030614 * A328615 A128016 A128017

Adjacent sequences: A381730 A381731 A381732 * A381734 A381735 A381736

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 05 2025

Status

approved