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A069153 Sum(d|n,d*(d-1)/2). 2
0, 1, 3, 7, 10, 19, 21, 35, 39, 56, 55, 91, 78, 113, 118, 155, 136, 208, 171, 252, 234, 287, 253, 395, 310, 404, 390, 497, 406, 614, 465, 651, 586, 698, 626, 910, 666, 875, 822, 1060, 820, 1202, 903, 1239, 1144, 1289, 1081, 1643, 1197, 1581, 1414, 1736 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Inverse Mobius transform of A000217. - R. J. Mathar, Jan 19 2009

LINKS

Table of n, a(n) for n=1..52.

FORMULA

G.f.: Sum_{k>0} x^(2*k)/(1-x^k)^3. - Vladeta Jovovic, Dec 17 2002

Row sums of triangle A134840. - Gary W. Adamson, Nov 12 2007

G.f. A(x) = (1/2) * x * d/dx log( B(x) ) where B() is g.f. for A052847. - Michael Somos, Feb 12 2008

G.f.: Sum_{k>0} ((k^2 - k) / 2) * x^k / (1 - x^k). - Michael Somos, Feb 12 2008

EXAMPLE

x^2 + 3*x^3 + 7*x^4 + 10*x^5 + 19*x^6 + 21*x^7 + 35*x^8 + 39*x^9 + 56*x^10 + ...

MATHEMATICA

A069153[n_]:=Plus@@Binomial[Divisors[n], 2]; Array[A069153, 100] (* Enrique Pérez Herrero, Feb 21 2012 *)

PROG

(PARI) {a(n) = if( n<1, 0, sumdiv(n, d, d^2 - d) / 2)}

CROSSREFS

Cf. A007437.

Cf. A134840.

Sequence in context: A171071 A265724 A024330 * A167390 A000223 A031328

Adjacent sequences:  A069150 A069151 A069152 * A069154 A069155 A069156

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Apr 08 2002

STATUS

approved

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Last modified April 18 10:44 EDT 2019. Contains 322209 sequences. (Running on oeis4.)