A082476 - OEIS

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A082476

a(n) = Sum_{d|n} mu(d)^2*tau(d)^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