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A175346
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a(n) = Sum_{k=1..n^2} d(k), d(k) = number of divisors of k (A000005).
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3
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1, 8, 23, 50, 87, 140, 201, 280, 373, 482, 605, 746, 897, 1070, 1261, 1466, 1689, 1932, 2189, 2468, 2761, 3074, 3405, 3764, 4127, 4518, 4925, 5360, 5807, 6276, 6757, 7262, 7789, 8342, 8915, 9502, 10107
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OFFSET
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1,2
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COMMENTS
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Generalized sequence: Sum_{k=1..T(n)} d(k). In this sequence T(n)=n^2, in A085831 T(n)=2^n, in A006218 T(n)=n. Other examples not in the OEIS: T(n)=p(n) n-th prime, T(n)=n*(n+1)/2 n-th triangular number, T(n)= F(n) n-th Fibonacci number, etc.
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LINKS
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FORMULA
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a(n) = n^2 + 2*Sum_{k=2..n} floor(n^2/k). - Chai Wah Wu, Oct 24 2023
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MATHEMATICA
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Table[Sum[DivisorSigma[0, k], {k, 1, n^2}], {n, 1, 80}] (* Carl Najafi, Aug 21 2011 *)
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PROG
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(Python)
def A175346(n): return (m:=n**2)+(sum(m//k for k in range(2, n+1))<<1) # Chai Wah Wu, Oct 24 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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