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A344329 Number of divisors of n^6. 2
1, 7, 7, 13, 7, 49, 7, 19, 13, 49, 7, 91, 7, 49, 49, 25, 7, 91, 7, 91, 49, 49, 7, 133, 13, 49, 19, 91, 7, 343, 7, 31, 49, 49, 49, 169, 7, 49, 49, 133, 7, 343, 7, 91, 91, 49, 7, 175, 13, 91, 49, 91, 7, 133, 49, 133, 49, 49, 7, 637, 7, 49, 91, 37, 49, 343, 7, 91, 49, 343, 7, 247, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

a(n) = A000005(A001014(n)).

Multiplicative with a(p^e) = 6*e+1.

a(n) = Sum_{d|n} 6^omega(d).

G.f.: Sum_{k>=1} 6^omega(k) * x^k/(1 - x^k).

Dirichlet g.f.: zeta(s)^2 * Product_{primes p} (1 + 5/p^s). - Vaclav Kotesovec, Aug 19 2021

MATHEMATICA

Table[DivisorSigma[0, n^6], {n, 1, 100}] (* Amiram Eldar, May 15 2021 *)

PROG

(PARI) a(n) = numdiv(n^6);

(PARI) a(n) = prod(k=1, #f=factor(n)[, 2], 6*f[k]+1);

(PARI) a(n) = sumdiv(n, d, 6^omega(d));

(PARI) my(N=99, x='x+O('x^N)); Vec(sum(k=1, N, 6^omega(k)*x^k/(1-x^k)))

(PARI) for(n=1, 100, print1(direuler(p=2, n, (1 + 5*X)/(1 - X)^2)[n], ", ")) \\ Vaclav Kotesovec, Aug 19 2021

CROSSREFS

Column k=6 of A343656.

Cf. A000005, A001014.

Sequence in context: A003883 A212535 A266116 * A116934 A143429 A168301

Adjacent sequences:  A344326 A344327 A344328 * A344330 A344331 A344332

KEYWORD

nonn,mult

AUTHOR

Seiichi Manyama, May 15 2021

STATUS

approved

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Last modified January 17 20:06 EST 2022. Contains 350410 sequences. (Running on oeis4.)