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

1,1

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)

Links

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

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

Example

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

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}]

Prog

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

Crossrefs

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

Sequence in context: A310190 A307203 A347638 * A043722 A288175 A214066

Adjacent sequences: A224877 A224878 A224879 * A224881 A224882 A224883

Keyword

nonn

Author

Hans Havermann, Jul 23 2013

Status

approved