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A224880 a(n) = 2n + sum of divisors of n. 8
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 (list; graph; refs; listen; history; text; internal format)
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 step 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

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, A075701, A155085, A237593, A245092, A299692.

Sequence in context: A319480 A310190 A307203 * A043722 A288175 A214066

Adjacent sequences:  A224877 A224878 A224879 * A224881 A224882 A224883

KEYWORD

nonn

AUTHOR

Hans Havermann, Jul 23 2013

STATUS

approved

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Last modified December 8 18:37 EST 2019. Contains 329865 sequences. (Running on oeis4.)