

A168013


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


4



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
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OFFSET

1,1


COMMENTS



LINKS



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)^21}];


PROG

(Python)
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



EXTENSIONS



STATUS

approved



