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
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
From Omar E. Pol, Sep 12 2025: (Start)
a(2^k) = 2^(k+2) - 1, k >= 0.
a(p) = 3*p + 1, if p is prime.
a(P) = 4*P, if P is a perfect number. (End)
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
KEYWORD
nonn
AUTHOR
Hans Havermann, Jul 23 2013
STATUS
approved