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A082476
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a(n)=sum(d|n, mu(d)^2*tau(d)^2).
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1
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1, 5, 5, 5, 5, 25, 5, 5, 5, 25, 5, 25, 5, 25, 25, 5, 5, 25, 5, 25, 25, 25, 5, 25, 5, 25, 5, 25, 5, 125, 5, 5, 25, 25, 25, 25, 5, 25, 25, 25, 5, 125, 5, 25, 25, 25, 5, 25, 5, 25, 25, 25, 5, 25, 25, 25, 25, 25, 5, 125, 5, 25, 25, 5, 25, 125, 5, 25, 25, 125, 5, 25, 5, 25, 25, 25, 25, 125
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listen;
history;
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internal format)
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OFFSET
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1,2
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COMMENTS
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More generally : sum(d|n, mu(d)^2*tau(d)^m)=(2^m+1)^omega(n)
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LINKS
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Table of n, a(n) for n=1..78.
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FORMULA
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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]
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MATHEMATICA
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Contribution from Enrique Pérez Herrero, Mar 29 2010: (Start)
tau[1, n_] := 1; SetAttributes[tau, Listable];
tau[k_, n_] := Plus @@ (tau[k - 1, Divisors[n]]) /; k > 1;
A082476[n_] := Abs[DivisorSum[n, MoebiusMu[ # ]*tau[3, #^2] &]];
(* or more easy *)
A082476[n_] := 5^PrimeNu[n] (End)
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PROG
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(PARI) a(n)=5^omega(n)
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CROSSREFS
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Cf. A074816.
Sequence in context: A076407 A134701 A078097 * A024729 A046271 A046263
Adjacent sequences: A082473 A082474 A082475 * A082477 A082478 A082479
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KEYWORD
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mult,nonn
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AUTHOR
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Benoit Cloitre, Apr 27 2003
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STATUS
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approved
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