A224880 a(n) = 2n + sum of divisors of n.

3, 7, 10, 15, 16, 24, 22, 31, 31, 38, 34, 52, 40, 52, 54, 63, 52, 75, 58, 82, 74, 80, 70, 108, 81, 94, 94, 112, 88, 132, 94, 127, 114, 122, 118, 163, 112, 136, 134, 170, 124, 180, 130, 172, 168, 164, 142, 220, 155, 193, 174, 202, 160, 228, 182, 232, 194, 206

Offset: 1

Author

Hans Havermann, Jul 23 2013

Keywords

• nonn

Comments

This sequence is A033880 for the negative integers, thus making explicit the mapping noted in A075701.

From Omar E. Pol, Jun 21 2018: (Start)

a(n) is also the total area of the terraces and the vertical sides that are visible in the perspective view at the n-th level (starting from the top) of the stepped pyramid described in A245092.

Partial sums give A299692. (End)

Examples

			a(6) = 2*6 + (1+2+3+6) = 24.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A033879, A033880, A072691, A075701, A155085, A237593, A245092, A299692.

Programs

Maple

with(numtheory); seq(2*k+sigma(k),k=1..100); # Wesley Ivan Hurt, Jul 24 2013

Mathematica

Table[2*n+DivisorSigma[1,n],{n,64}]

PARI

vector(80, n, 2*n + sigma(n)) \\ Michel Marcus, Aug 19 2015

Formula

a(n) = A155085(n) + n.

a(n) = 2n + sigma(n) = A005843(n) + A000203(n) = A033879(n) + 2*A000203(n) = A033880(n) + 2*A005843(n) = 2*A155085(n) - A000203(n) = 2*A000203(n) - A033880(n). - Wesley Ivan Hurt, Jul 24 2013

G.f.: 2*x/(1 - x)^2 + Sum_{k>=1} x^k/(1 - x^k)^2. - Ilya Gutkovskiy, Mar 17 2017

a(n) = A001065(n) + A008585(n). - Omar E. Pol, Mar 06 2018

Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = zeta(2)/2 + 1 = A072691 + 1 = 1.822467... . - Amiram Eldar, Mar 17 2024