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A082476 a(n) = Sum_{d|n} mu(d)^2*tau(d)^2. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

More generally : sum(d|n, mu(d)^2*tau(d)^m) = (2^m+1)^omega(n).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n

FORMULA

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

MATHEMATICA

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 *)

PROG

(PARI) a(n)=5^omega(n)

CROSSREFS

Cf. A000005, A000351, A001221, A007425, A007947, A008683, A061200, A074816.

Sequence in context: A078097 A285243 A282209 * A024729 A046271 A283076

Adjacent sequences:  A082473 A082474 A082475 * A082477 A082478 A082479

KEYWORD

mult,nonn

AUTHOR

Benoit Cloitre, Apr 27 2003

STATUS

approved

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Last modified July 22 06:22 EDT 2019. Contains 325213 sequences. (Running on oeis4.)