A343526 Number of divisors of n^7.
1, 8, 8, 15, 8, 64, 8, 22, 15, 64, 8, 120, 8, 64, 64, 29, 8, 120, 8, 120, 64, 64, 8, 176, 15, 64, 22, 120, 8, 512, 8, 36, 64, 64, 64, 225, 8, 64, 64, 176, 8, 512, 8, 120, 120, 64, 8, 232, 15, 120, 64, 120, 8, 176, 64, 176, 64, 64, 8, 960, 8, 64, 120, 43, 64, 512, 8, 120, 64, 512, 8
Offset: 1
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Table[DivisorSigma[0, n^7], {n, 1, 100}] (* Amiram Eldar, May 15 2021 *) -
PARI
a(n) = numdiv(n^7);
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PARI
a(n) = prod(k=1, #f=factor(n)[, 2], 7*f[k]+1);
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PARI
a(n) = sumdiv(n, d, 7^omega(d));
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PARI
my(N=99, x='x+O('x^N)); Vec(sum(k=1, N, 7^omega(k)*x^k/(1-x^k))) -
PARI
for(n=1, 100, print1(direuler(p=2, n, (1 + 6*X)/(1 - X)^2)[n], ", ")) \\ Vaclav Kotesovec, Aug 19 2021
Formula
Multiplicative with a(p^e) = 7*e+1.
a(n) = Sum_{d|n} 7^omega(d).
G.f.: Sum_{k>=1} 7^omega(k) * x^k/(1 - x^k).
Dirichlet g.f.: zeta(s)^2 * Product_{primes p} (1 + 6/p^s). - Vaclav Kotesovec, Aug 19 2021