A168013 a(n) = Sum of all divisors of all numbers < (n+1)^2.

8, 56, 189, 491, 1007, 1930, 3276, 5314, 8082, 11973, 16783, 23355, 31314, 41380, 53566, 68510, 85771, 106981, 130973, 159470, 192020, 229762, 271873, 320779, 375031, 436311, 504464, 581422, 664364, 759025, 860907, 973989, 1097783

Offset

1,1

Comments

Partial sums of A168012.

Links

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

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

Cf. A000203, A024916, A168010, A168011, A168012.

Sequence in context: A355948 A267522 A073831 * A003210 A135417 A248332

Adjacent sequences: A168010 A168011 A168012 * A168014 A168015 A168016

Keyword

nonn

Author

Omar E. Pol, Nov 16 2009

Extensions

More terms from Sean A. Irvine, Dec 07 2009

Status

approved