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A196524 Phi(n)*tau(n^2). 2
1, 3, 6, 10, 12, 18, 18, 28, 30, 36, 30, 60, 36, 54, 72, 72, 48, 90, 54, 120, 108, 90, 66, 168, 100, 108, 126, 180, 84, 216, 90, 176, 180, 144, 216, 300, 108, 162, 216, 336, 120, 324, 126, 300, 360, 198, 138, 432, 210, 300, 288, 360, 156, 378, 360, 504, 324, 252, 174, 720, 180, 270, 540, 416, 432, 540 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Multiplicative with a(p^e) = (2e+1)*(p-1)*p^(e-1), e>0.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

J. M. Borwein, K.-K. S. Choi, On Dirichlet series for sums of squares, Ramanujan J. 7 (1-3) (2003) 95-127

FORMULA

a(n) = A048691(n)*A000010(n).

Dirichlet g.f.: zeta^3(s-1)*product_{primes p} (1-3/p^s -1/p^(2s-2) +4/p^(2s-1) -1/p^(3s-2)) = zeta^2(s-1)*product_{primes p} (1 +p^(1-s) +p^(1-2s) -3p^(-s)).

MATHEMATICA

Table[EulerPhi[n] DivisorSigma[0, n^2], {n, 70}] (* Alonso del Arte, Oct 07 2011 *)

PROG

(PARI) a(n)=numdiv(n^2)*eulerphi(n) \\ Charles R Greathouse IV, Dec 07 2011

CROSSREFS

Sequence in context: A287176 A310045 A310046 * A082925 A131696 A164114

Adjacent sequences:  A196521 A196522 A196523 * A196525 A196526 A196527

KEYWORD

mult,nonn,easy

AUTHOR

R. J. Mathar, Oct 07 2011

STATUS

approved

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Last modified April 19 04:19 EDT 2019. Contains 322237 sequences. (Running on oeis4.)