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A069097 Moebius transform of A064987, n*sigma(n). 11
1, 5, 11, 22, 29, 55, 55, 92, 105, 145, 131, 242, 181, 275, 319, 376, 305, 525, 379, 638, 605, 655, 551, 1012, 745, 905, 963, 1210, 869, 1595, 991, 1520, 1441, 1525, 1595, 2310, 1405, 1895, 1991, 2668, 1721, 3025, 1891, 2882, 3045, 2755, 2255, 4136, 2737 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Equals A127569 * [1, 2, 3,...]. - Gary W. Adamson, Jan 19 2007

Equals row sums of triangle A143309 and of triangle A143312. [Gary W. Adamson, Aug 06 2008]

Dirichlet convolution of A000290 and A000010 (see Jovovic formula) with Dirichlet g.f. zeta(s-2)*zeta(s-1)/zeta(s). - R. J. Mathar, Feb 03 2011

LINKS

Table of n, a(n) for n=1..49.

FORMULA

a(n) = Sum_{d|n} d^2*phi(n/d). - Vladeta Jovovic, Jul 31 2002

a(n) = Sum_{k=1..n} gcd(n, k)^2. - Vladeta Jovovic, Aug 27 2003

a(n) = n*Sum_{d|n} J_2(d)/d, where J_2 is A007434. - Enrique Pérez Herrero, Feb 25 2012.

G.f.: sum {n >= 1} phi(n)*(x^n + x^(2*n))/(1 - x^n)^3 = x + 5*x^2 + 11*x^3 + 22*x^4  + .... - Peter Bala, Dec 30 2013

Multiplicative with a(p^e) = p^(e-1)*(p^e*(p+1)-1). - R. J. Mathar, Jun 23 2018

MATHEMATICA

A069097[n_]:=n^2*Plus @@((EulerPhi[#]/#^2)&/@ Divisors[n]); Array[A069097, 100] (* Enrique Pérez Herrero, Feb 25 2012 *)

PROG

(PARI) for(n=1, 100, print1((sumdiv(n, k, k*sigma(k)*moebius(n/k))), ", "))

CROSSREFS

Cf. A033457, A068963.

Cf. A127569.

Cf. A143309, A143312. [Gary W. Adamson, Aug 06 2008]

Sequence in context: A296033 A296968 A184552 * A222548 A024921 A189978

Adjacent sequences:  A069094 A069095 A069096 * A069098 A069099 A069100

KEYWORD

easy,nonn,mult

AUTHOR

Benoit Cloitre, Apr 05 2002

STATUS

approved

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Last modified July 6 23:56 EDT 2020. Contains 335484 sequences. (Running on oeis4.)