login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A086666 a(n) = sigma_2(n) - sigma_1(n). 2
0, 2, 6, 14, 20, 38, 42, 70, 78, 112, 110, 182, 156, 226, 236, 310, 272, 416, 342, 504, 468, 574, 506, 790, 620, 808, 780, 994, 812, 1228, 930, 1302, 1172, 1396, 1252, 1820, 1332, 1750, 1644, 2120, 1640, 2404, 1806, 2478, 2288, 2578, 2162, 3286, 2394, 3162 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Joerg Arndt, On computing the generalized Lambert series, arXiv:1202.6525v3 [math.CA], (2012).

FORMULA

G.f.: Sum_{n>=1} n*(n-1) * x^n/(1-x^n). - Joerg Arndt, Jan 30, 2011

L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k-1)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 21 2018

From Peter Bala, Jan 21 20221; (Start)

a(n) = 2*A069153(n).

G.f.: A(x) = Sum_{n >= 1} 2*x^(2*n)/(1 - x^n)^3.

A faster converging series: A(x) = Sum_{n >= 1} x^(n^2)*( n*(n-1)*x^(3*n) - (n^2 + n - 2)*x^(2*n) + n*(3 - n)*x^n + n*(n - 1) )/(1 - x^n)^3 - differentiate equation 5 in Arndt twice w.r.t x and set x = 1. (End)

MATHEMATICA

Table[DivisorSigma[2, n]-DivisorSigma[1, n], {n, 50}] (* Harvey P. Dale, Aug 01 2020 *)

PROG

(PARI) for (n=2, 50, print1(sigma(n, 2)-sigma(n, 1)", "))

CROSSREFS

Cf. A000203, A001157, A052847, A069153, A092348.

Sequence in context: A107369 A151731 A009779 * A032383 A014775 A009218

Adjacent sequences:  A086663 A086664 A086665 * A086667 A086668 A086669

KEYWORD

nonn,easy

AUTHOR

Jon Perry, Jul 27 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 30 00:57 EDT 2021. Contains 346346 sequences. (Running on oeis4.)