

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
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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 nth 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



