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A344335
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Number of divisors of n^8.
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2
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1, 9, 9, 17, 9, 81, 9, 25, 17, 81, 9, 153, 9, 81, 81, 33, 9, 153, 9, 153, 81, 81, 9, 225, 17, 81, 25, 153, 9, 729, 9, 41, 81, 81, 81, 289, 9, 81, 81, 225, 9, 729, 9, 153, 153, 81, 9, 297, 17, 153, 81, 153, 9, 225, 81, 225, 81, 81, 9, 1377, 9, 81, 153, 49, 81, 729, 9, 153, 81, 729, 9
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OFFSET
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1,2
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LINKS
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FORMULA
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Multiplicative with a(p^e) = 8*e+1.
a(n) = Sum_{d|n} 8^omega(d).
G.f.: Sum_{k>=1} 8^omega(k) * x^k/(1 - x^k).
Dirichlet g.f.: zeta(s)^2 * Product_{primes p} (1 + 7/p^s). - Vaclav Kotesovec, Aug 19 2021
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MATHEMATICA
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Table[DivisorSigma[0, n^8], {n, 1, 100}] (* Amiram Eldar, May 15 2021 *)
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PROG
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(PARI) a(n) = numdiv(n^8);
(PARI) a(n) = prod(k=1, #f=factor(n)[, 2], 8*f[k]+1);
(PARI) a(n) = sumdiv(n, d, 8^omega(d));
(PARI) my(N=99, x='x+O('x^N)); Vec(sum(k=1, N, 8^omega(k)*x^k/(1-x^k)))
(PARI) for(n=1, 100, print1(direuler(p=2, n, (1 + 7*X)/(1 - X)^2)[n], ", ")) \\ Vaclav Kotesovec, Aug 19 2021
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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