%I #40 Mar 17 2024 03:10:04

%S 3,7,10,15,16,24,22,31,31,38,34,52,40,52,54,63,52,75,58,82,74,80,70,

%T 108,81,94,94,112,88,132,94,127,114,122,118,163,112,136,134,170,124,

%U 180,130,172,168,164,142,220,155,193,174,202,160,228,182,232,194,206

%N a(n) = 2n + sum of divisors of n.

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

%C From _Omar E. Pol_, Jun 21 2018: (Start)

%C 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.

%C Partial sums give A299692. (End)

%H T. D. Noe, <a href="/A224880/b224880.txt">Table of n, a(n) for n = 1..10000</a>

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

%F 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

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

%F a(n) = A001065(n) + A008585(n). - _Omar E. Pol_, Mar 06 2018

%F 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

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

%p with(numtheory); seq(2*k+sigma(k),k=1..100); # _Wesley Ivan Hurt_, Jul 24 2013

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

%o (PARI) vector(80, n, 2*n + sigma(n)) \\ _Michel Marcus_, Aug 19 2015

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

%K nonn

%O 1,1

%A _Hans Havermann_, Jul 23 2013