A332264 Partial sums of A334136.

0, 3, 11, 32, 56, 116, 164, 269, 373, 535, 655, 963, 1131, 1443, 1779, 2244, 2532, 3195, 3555, 4353, 4993, 5749, 6277, 7657, 8401, 9451, 10491, 12003, 12843, 14931, 15891, 17844, 19380, 21162, 22794, 25979, 27347, 29567, 31695, 35205, 36885, 40821, 42669, 46281, 49713, 52953, 55161, 60989, 63725, 68282

Offset: 1

Author

Omar E. Pol, Apr 19 2020

Keywords

• nonn

Comments

a(n) is also the volume after n-th step of the symmetric staircase described in A244580 except the volume of the base level.

Examples

			For n = 4 the volume of the first four levels of the symmetric staircase described in A244580 is 47, since the structure contains 47 cubes. The volume of the base level is 15, since the base of the structure contains 15 cubes, so a(4) = 47 - 15 = 32.
		

Crossrefs

Cf. A000203, A024916, A064987, A143128, A175254, A237593, A244580, A256533, A334136.

Programs

PARI

a(n) = sum(k=1, n, (k-1)*sigma(k)); \\ Michel Marcus, Apr 19 2020

Python

from math import isqrt
def A332264(n): return (((s:=isqrt(n))**2*(s+1)*(6-(s+1)*((s<<1)+1))>>1)+sum((q:=n//k)*(k*(q+1)*(3*k+(q<<1)+1)-3*((k<<1)+q+1)) for k in range(1,s+1)))//6 # Chai Wah Wu, Oct 25 2023

Formula

a(n) = A143128(n) - A024916(n).

a(n) = A256533(n) - A175254(n). - Omar E. Pol, Apr 29 2020