A344329 Number of divisors of n^6.
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
Offset: 1
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Table[DivisorSigma[0, n^6], {n, 1, 100}] (* Amiram Eldar, May 15 2021 *) -
PARI
a(n) = numdiv(n^6);
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PARI
a(n) = prod(k=1, #f=factor(n)[, 2], 6*f[k]+1);
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PARI
a(n) = sumdiv(n, d, 6^omega(d));
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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
Formula
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