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A082476
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a(n) = Sum_{d|n} mu(d)^2*tau(d)^2.
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4
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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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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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Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences computed from exponents in factorization of n
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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. - Enrique Pérez Herrero, Mar 29 2010
a(n) = tau_5(rad(n)) = A061200(A007947(n)). - Enrique Pérez Herrero, Jun 24 2010
a(n) = A000351(A001221(n)). - Antti Karttunen, Jul 26 2017
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MATHEMATICA
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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] &]]; (* Enrique Pérez Herrero, Mar 29 2010 *)
(* or more easy *)
A082476[n_] := 5^PrimeNu[n] (* Enrique Pérez Herrero, Mar 29 2010 *)
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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. A000005, A000351, A001221, A007425, A007947, A008683, A061200, A074816.
Sequence in context: A285243 A339704 A282209 * A024729 A046271 A341600
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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