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A224880
a(n) = 2n + sum of divisors of n.
9
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)
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
KEYWORD
nonn
AUTHOR
Hans Havermann, Jul 23 2013
STATUS
approved