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A359040
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Sum of the number of divisors of floor(n/(b*c)) with b,c > 0 and b*c <= n.
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1
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1, 4, 6, 12, 13, 21, 21, 32, 34, 39, 39, 59, 57, 61, 63, 80, 79, 94, 92, 107, 105, 107, 107, 149, 145, 144, 146, 158, 156, 176, 172, 199, 197, 197, 195, 239, 234, 234, 230, 263, 259, 273, 269, 279, 280, 280, 280, 354, 346, 346, 342, 346, 344
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OFFSET
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1,2
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LINKS
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FORMULA
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Li & Karras prove that a(n) = An log n + Bn + O(n^e) for any e > 10/17, where A and B are defined in their paper (see Links). This sharpens a general result of Bourgain & Watt.
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PROG
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(PARI) a(n)=2*sum(a=1, n, my(N=n\a); sum(b=1, min(a-1, N), numdiv(N\b))) + sum(a=1, sqrtint(n), numdiv(n\a^2))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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