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A344328
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Number of divisors of n^5.
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2
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1, 6, 6, 11, 6, 36, 6, 16, 11, 36, 6, 66, 6, 36, 36, 21, 6, 66, 6, 66, 36, 36, 6, 96, 11, 36, 16, 66, 6, 216, 6, 26, 36, 36, 36, 121, 6, 36, 36, 96, 6, 216, 6, 66, 66, 36, 6, 126, 11, 66, 36, 66, 6, 96, 36, 96, 36, 36, 6, 396, 6, 36, 66, 31, 36, 216, 6, 66, 36, 216, 6, 176, 6, 36, 66, 66, 36
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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) = 5*e+1.
a(n) = Sum_{d|n} 5^omega(d).
G.f.: Sum_{k>=1} 5^omega(k) * x^k/(1 - x^k).
Dirichlet g.f.: zeta(s)^2 * Product_{primes p} (1 + 4/p^s). - Vaclav Kotesovec, Aug 19 2021
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MATHEMATICA
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Table[DivisorSigma[0, n^5], {n, 1, 100}] (* Amiram Eldar, May 15 2021 *)
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PROG
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(PARI) a(n) = numdiv(n^5);
(PARI) a(n) = prod(k=1, #f=factor(n)[, 2], 5*f[k]+1);
(PARI) a(n) = sumdiv(n, d, 5^omega(d));
(PARI) my(N=99, x='x+O('x^N)); Vec(sum(k=1, N, 5^omega(k)*x^k/(1-x^k)))
(PARI) for(n=1, 100, print1(direuler(p=2, n, (1 + 4*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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