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A161841
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Number of factors, with repetition, in all distinct pairs (a <= b) such that a*b = n.
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7
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2, 2, 2, 4, 2, 4, 2, 4, 4, 4, 2, 6, 2, 4, 4, 6, 2, 6, 2, 6, 4, 4, 2, 8, 4, 4, 4, 6, 2, 8, 2, 6, 4, 4, 4, 10, 2, 4, 4, 8, 2, 8, 2, 6, 6, 4, 2, 10, 4, 6, 4, 6, 2, 8, 4, 8, 4, 4, 2, 12, 2, 4, 6, 8, 4, 8, 2, 6, 4, 8, 2, 12, 2, 4, 6, 6, 4, 8, 2, 10, 6, 4, 2, 12, 4, 4, 4, 8, 2, 12, 4, 6, 4, 4, 4, 12, 2, 6, 6, 10
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OFFSET
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1,1
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ (log(n) + 2*gamma - 1)*n + sqrt(n), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jul 01 2021
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EXAMPLE
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a(16)=6 because there are three distinct pairs (a <= b) such that a*b = n: the pairs (1,16), (2,8) and (4,4). So the number of factors, with repetition, in all the pairs is equal to 6.
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MAPLE
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seq(numtheory:-tau(n) + `if`(issqr(n), 1, 0), n = 1 .. 200); # Robert Israel, Dec 23 2015
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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