A344337 a(n) = 9^omega(n), where omega(n) is the number of distinct primes dividing n.

1, 9, 9, 9, 9, 81, 9, 9, 9, 81, 9, 81, 9, 81, 81, 9, 9, 81, 9, 81, 81, 81, 9, 81, 9, 81, 9, 81, 9, 729, 9, 9, 81, 81, 81, 81, 9, 81, 81, 81, 9, 729, 9, 81, 81, 81, 9, 81, 9, 81, 81, 81, 9, 81, 81, 81, 81, 81, 9, 729, 9, 81, 81, 9, 81, 729, 9, 81, 81, 729, 9, 81, 9, 81, 81, 81

Offset

1,2

Links

Table of n, a(n) for n=1..76.

Formula

a(n) = A001019(A001221(n)).

Multiplicative with a(p^e) = 9.

a(n) = Sum_{d|n} mu(d)^2 * tau(d)^3.

Dirichlet g.f.: Product_{p prime} (1 + 9/(p^s-1)). - Amiram Eldar, Sep 19 2023

Mathematica

Table[9^PrimeNu[n], {n, 1, 100}] (* Amiram Eldar, May 15 2021 *)

Prog

(PARI) a(n) = 9^omega(n);
(PARI) a(n) = prod(k=1, #f=factor(n)[, 2], 9);
(PARI) a(n) = sumdiv(n, d, moebius(d)^2*numdiv(d)^3);

Crossrefs

k^omega(n): A034444 (k=2), A074816 (k=3), A082476 (k=5), this sequence (k=9).

Cf. A000005, A001019, A001221.

Sequence in context: A242893 A275485 A346263 * A293832 A277223 A144586

Adjacent sequences: A344334 A344335 A344336 * A344338 A344339 A344340

Keyword

nonn,mult

Author

Seiichi Manyama, May 15 2021

Status

approved