A168011 a(n) = Sum of all numbers of divisors of all numbers < (n+1)^2.

5, 20, 45, 84, 131, 198, 273, 368, 473, 602, 731, 894, 1061, 1252, 1457, 1686, 1917, 2186, 2453, 2752, 3065, 3402, 3743, 4122, 4509, 4918, 5345, 5804, 6249, 6754, 7251, 7780, 8333, 8906, 9477, 10104, 10729, 11386, 12047, 12758, 13445, 14202, 14945

Offset: 1

Author

Omar E. Pol, Nov 16 2009

Keywords

• nonn

Comments

Partial sums of A168010.

Examples

			a(2)=20 because the numbers < (2+1)^2 are 1,2,3,4,5,6,7 and 8. Then a(2) = d(1)+d(2)+d(3)+d(4)+d(5)+d(6)+d(7)+d(8) = 1+2+2+3+2+4+2+4 = 20, where d(n) is the number of divisor of n (see A000005).
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A168010, A168012, A168013.

Programs

Mathematica

f[n_] := Plus @@ DivisorSigma[0, Range[(n + 1)^2 - 1]]; Array[f, 43] (* Robert G. Wilson v, Dec 10 2009 *)

Python

def A168011(n):
    m = n*(n+2)
    return (sum(m//k for k in range(1,n+1))<<1)-n**2 # Chai Wah Wu, Oct 23 2023

Extensions

More terms from Robert G. Wilson v, Dec 10 2009