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A328366
a(n) is the surface area of the stepped pyramid with n levels described in A245092.
3
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
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
KEYWORD
nonn
AUTHOR
Omar E. Pol, Oct 26 2019
STATUS
approved