OFFSET
1,2
COMMENTS
Partial sums of A024916. - Omar E. Pol, Jul 03 2014
a(n) is also the volume of the stepped pyramid with n levels described in A245092. - Omar E. Pol, Aug 12 2015
Also the alternating row sums of A262612. - Omar E. Pol, Nov 23 2015
From Omar E. Pol, Jan 20 2021: (Start)
Antidiagonal sums of A319073.
Row sums of A274824. (End)
Row sums of A345272. - Omar E. Pol, Jun 14 2021
Also the alternating row sums of A353690. - Omar E. Pol, Jun 05 2022
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 2209 terms from Indranil Ghosh)
FORMULA
Conjecture: a(n) = Sum_{k=0..n} A006218(n-k). - R. J. Mathar, Oct 17 2012
a(n) ~ Pi^2*n^3/36. - Vaclav Kotesovec, Sep 25 2016
G.f.: (1/(1 - x)^2)*Sum_{k>=1} k*x^k/(1 - x^k). - Ilya Gutkovskiy, Jan 03 2017
a(n) = Sum_{k=1..n} Sum_{i=1..k} k - (k mod i). - Wesley Ivan Hurt, Sep 13 2017
a(n) = A244050(n)/4. - Omar E. Pol, Jan 22 2021
EXAMPLE
For n = 4: a(4) = sigma(1)*4 + sigma(2)*3 + sigma(3)*2 + sigma(4)*1 = 1*4 + 3*3 + 4*2 + 7*1 = 28.
MAPLE
b:= proc(n) option remember; `if`(n<1, [0$2],
(p-> p+[numtheory[sigma](n), p[1]])(b(n-1)))
end:
a:= n-> b(n+1)[2]:
seq(a(n), n=1..45); # Alois P. Heinz, Oct 07 2021
MATHEMATICA
Table[Sum[DivisorSigma[1, k] (n - k + 1), {k, n}], {n, 45}] (* Michael De Vlieger, Nov 24 2015 *)
PROG
(PARI) a(n) = sum(x=1, n, sigma(x)*(n-x+1)) \\ Michel Marcus, Mar 18 2013
(Python)
from math import isqrt
def A175254(n): return (((s:=isqrt(n))**2*(s+1)*((s+1)*(2*s+1)-6*(n+1))>>1) + sum((q:=n//k)*(-k*(q+1)*(3*k+2*q+1)+3*(n+1)*(2*k+q+1)) for k in range(1, s+1)))//6 # Chai Wah Wu, Oct 21 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jaroslav Krizek, Mar 14 2010
EXTENSIONS
Corrected by Jaroslav Krizek, Mar 17 2010
More terms from Michel Marcus, Mar 18 2013
STATUS
approved