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From Vaclav Kotesovec, Feb 28 2023: (Start)
Dirichlet g.f.: Product_{primes p} (1 + 5/(p^s - 1)).
Dirichlet g.f.: zeta(s)^5 * Product_{primes p} (1 - 10/p^(2*s) + 20/p^(3*s) - 15/p^(4*s) + 4/p^(5*s)), (with a product that converges for s=1). (End)
(PARI) for(n=1, 100, print1(direuler(p=2, n, (4*X+1)/(1-X))[n], ", ")) \\ Vaclav Kotesovec, Feb 28 2023
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a(n) = sum(Sum_{d|n, } mu(d)^2*tau(d)^2).
a(n) = 5^omega(n); multiplicative with a(p^e)=5.
a(n) = abs(sum(d|n, mu(d)*tau_3(d^2))), where tau_3 is A007425. - From __Enrique Pérez Herrero_, Mar 29 2010
Contribution from Enrique Pérez Herrero, Mar 29 2010: (Start)
A082476[n_] := Abs[DivisorSum[n, MoebiusMu[ # ]*tau[3, #^2] &]]; (* _Enrique Pérez Herrero_, Mar 29 2010 *)
A082476[n_] := 5^PrimeNu[n] (End* _Enrique Pérez Herrero_, Mar 29 2010 *)
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a(n) = sum(d|n, mu(d)^2*tau(d)^2).
More generally : sum(d|n, mu(d)^2*tau(d)^m) = (2^m+1)^omega(n).
Antti Karttunen, <a href="/A082476/b082476.txt">Table of n, a(n) for n = 1..10000</a>
<a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
a(n) = 5^omega(n); multiplicative with a(p^e)=5
a(n) = abs(sum(d|n, mu(d)*tau_3(d^2))), where tau_3 is A007425 [. - From Enrique Pérez Herrero, Mar 29 2010]
a(n) = tau_5(rad(n)) = A061200(A007947(n)) [From _. - _Enrique Pérez Herrero_, Jun 24 2010]
a(n) = A000351(A001221(n)). - Antti Karttunen, Jul 26 2017
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Contribution from _Enrique Perez Pérez Herrero (psychgeometry(AT)gmail.com), _, Mar 29 2010: (Start)