OFFSET
1,1
COMMENTS
Partial sums of A168012.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A024916(n^2+2*n). - Jason Yuen, Oct 08 2024
EXAMPLE
For n=2 the a(2)=56 because the numbers < (2+1)^2 are 1,2,3,4,5,6,7 and 8. Then a(2) = sigma(1)+sigma(2)+sigma(3)+sigma(4)+sigma(5)+sigma(6)+sigma(7)+sigma(8) = 1+3+4+7+6+12+8+15 = 56, where sigma(n) is the sum of divisor of n (see A000203).
MATHEMATICA
A168012[n_]:=Sum[DivisorSigma[1, k], {k, n^2, (n+1)^2-1}];
Accumulate[Array[A168012, 50]] (* Paolo Xausa, Oct 23 2023 *)
PROG
(Python)
def A168013(n):
m = n*(n+2)
return sum((q:=m//k)*((k<<1)+q+1) for k in range(1, n+1))-n**2*(n+1)>>1 # Chai Wah Wu, Oct 23 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Nov 16 2009
EXTENSIONS
More terms from Sean A. Irvine, Dec 07 2009
STATUS
approved