A328366 a(n) is the surface area of the stepped pyramid with n levels described in A245092.

6, 20, 40, 70, 102, 150, 194, 256, 318, 394, 462, 566, 646, 750, 858, 984, 1088, 1238, 1354, 1518, 1666, 1826, 1966, 2182, 2344, 2532, 2720, 2944, 3120, 3384, 3572, 3826, 4054, 4298, 4534, 4860, 5084, 5356, 5624, 5964, 6212, 6572, 6832, 7176, 7512, 7840, 8124, 8564, 8874, 9260, 9608, 10012

Offset

1,1

Links

Table of n, a(n) for n=1..52.

Formula

a(n) = 4*A000217(n) + 2*A024916(n).

a(n) = 2*(A002378(n) + A327329(n)).

a(n) = 2*(A045943(n) + A153485(n)).

a(n) = A046092(n) + A327329(n).

a(n) = 2*A299692(n).

a(n) = c * n^2 + O(n*log(n)), where c = zeta(2) + 2 = 3.644934... . - Amiram Eldar, Mar 21 2024

Example

For n = 1 the first level of the stepped pyramid is a cube, so a(1) = 6.

Mathematica

s=0; Do[s=s+4*DivisorSigma[1, n]; t=2n(n+1); Print[(s/2)+t], {n, 1, 8000}] (* Metin Sariyar, Nov 20 2019 *)

Prog

(Python)
from math import isqrt
def A328366(n): return (n*(n+1)<<1)-(s:=isqrt(n))**2*(s+1)+sum((q:=n//k)*((k<<1)+q+1) for k in range(1, s+1)) # Chai Wah Wu, Oct 22 2023

Crossrefs

Cf. A000217, A002378, A013661, A024916, A045943, A046092, A153485, A175254 (volume), A196020, A235791, A236104, A237270, A237271, A237591, A237593, A245092, A262626, A299692, A327329.

Sequence in context: A031068 A031052 A097811 * A369348 A143711 A338120

Adjacent sequences: A328363 A328364 A328365 * A328367 A328368 A328369

Keyword

nonn

Author

Omar E. Pol, Oct 26 2019

Status

approved