A344336 Number of divisors of n^9.

1, 10, 10, 19, 10, 100, 10, 28, 19, 100, 10, 190, 10, 100, 100, 37, 10, 190, 10, 190, 100, 100, 10, 280, 19, 100, 28, 190, 10, 1000, 10, 46, 100, 100, 100, 361, 10, 100, 100, 280, 10, 1000, 10, 190, 190, 100, 10, 370, 19, 190, 100, 190, 10, 280, 100, 280, 100, 100, 10, 1900, 10, 100

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000005(A001017(n)).

Multiplicative with a(p^e) = 9*e+1.

a(n) = Sum_{d|n} 9^omega(d).

G.f.: Sum_{k>=1} 9^omega(k) * x^k/(1 - x^k).

Dirichlet g.f.: zeta(s)^2 * Product_{primes p} (1 + 8/p^s). - Vaclav Kotesovec, Aug 19 2021

Mathematica

Table[DivisorSigma[0, n^9], {n, 1, 100}] (* Amiram Eldar, May 15 2021 *)

Prog

(PARI) a(n) = numdiv(n^9);
(PARI) a(n) = prod(k=1, #f=factor(n)[, 2], 9*f[k]+1);
(PARI) a(n) = sumdiv(n, d, 9^omega(d));
(PARI) my(N=99, x='x+O('x^N)); Vec(sum(k=1, N, 9^omega(k)*x^k/(1-x^k)))
(PARI) for(n=1, 100, print1(direuler(p=2, n, (1 + 8*X)/(1 - X)^2)[n], ", ")) \\ Vaclav Kotesovec, Aug 19 2021

Crossrefs

Column k=9 of A343656.

Cf. A000005, A001017, A344337 (9^omega(n)).

Sequence in context: A352314 A363328 A047879 * A168416 A141324 A097041

Adjacent sequences: A344333 A344334 A344335 * A344337 A344338 A344339

Keyword

nonn,mult

Author

Seiichi Manyama, May 15 2021

Status

approved