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A086671
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Sum of floor(sqrt(d)) where d runs through the divisors of n.
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9
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1, 2, 2, 4, 3, 5, 3, 6, 5, 7, 4, 10, 4, 7, 7, 10, 5, 12, 5, 13, 8, 9, 5, 16, 8, 10, 10, 14, 6, 18, 6, 15, 10, 11, 10, 23, 7, 12, 11, 21, 7, 20, 7, 17, 16, 12, 7, 26, 10, 19, 13, 19, 8, 24, 13, 23, 13, 14, 8, 34, 8, 14, 18, 23, 14, 25, 9, 21, 14, 25, 9, 37, 9
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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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G.f.: sum(k>=1, floor(sqrt(k))*x^k/(1-x^k) ). - Mircea Merca, Feb 22 2014
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EXAMPLE
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10 has divisors 1,2,5,10. floor(sqrt(d)) gives 1,1,2,3, therefore a(10)=7.
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MAPLE
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add(floor(sqrt(d)), d = numtheory[divisors](n))
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MATHEMATICA
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Table[DivisorSum[n, Floor[Sqrt[#]] &], {n, 100}] (* T. D. Noe, Oct 28 2013 *)
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PROG
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(PARI) for (n=1, 100, s=0; fordiv(i=n, i, s+=floor(sqrt(i))); print1(", "s))
(PARI) a(n) = sumdiv(n, d, sqrtint(d)); \\ Michel Marcus, Mar 03 2020
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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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