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 A168011 a(n) = Sum of all numbers of divisors of all numbers < (n+1)^2. 5

%I #15 Oct 23 2023 11:37:12

%S 5,20,45,84,131,198,273,368,473,602,731,894,1061,1252,1457,1686,1917,

%T 2186,2453,2752,3065,3402,3743,4122,4509,4918,5345,5804,6249,6754,

%U 7251,7780,8333,8906,9477,10104,10729,11386,12047,12758,13445,14202,14945

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

%C Partial sums of A168010.

%H Chai Wah Wu, <a href="/A168011/b168011.txt">Table of n, a(n) for n = 1..10000</a>

%e 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).

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

%o (Python)

%o def A168011(n):

%o m = n*(n+2)

%o return (sum(m//k for k in range(1,n+1))<<1)-n**2 # _Chai Wah Wu_, Oct 23 2023

%Y Cf. A000005, A168010, A168012, A168013.

%K nonn

%O 1,1

%A _Omar E. Pol_, Nov 16 2009

%E More terms from _Robert G. Wilson v_, Dec 10 2009

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Last modified November 28 22:38 EST 2023. Contains 367422 sequences. (Running on oeis4.)