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A344137
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Sum of the squarefree divisors of n whose square does not divide n.
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3
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0, 2, 3, 0, 5, 11, 7, 0, 0, 17, 11, 9, 13, 23, 23, 0, 17, 8, 19, 15, 31, 35, 23, 9, 0, 41, 0, 21, 29, 71, 31, 0, 47, 53, 47, 0, 37, 59, 55, 15, 41, 95, 43, 33, 20, 71, 47, 9, 0, 12, 71, 39, 53, 8, 71, 21, 79, 89, 59, 69, 61, 95, 28, 0, 83, 143, 67, 51, 95, 143, 71, 0, 73
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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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a(n) = Sum_{d|n} d * mu(d)^2 * c(n/d^2), where c(n) = ceiling(n) - floor(n).
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EXAMPLE
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a(20) = Sum_{d|20} d * mu(d)^2 * c(20/d^2) = 1*1*0 + 2*1*0 + 4*0*1 + 5*1*1 + 10*1*1 + 20*0*1 = 15.
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MATHEMATICA
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a[n_] := DivisorSum[n, # &, SquareFreeQ[#] && ! Divisible[n, #^2] &]; Array[a, 100] (* Amiram Eldar, Oct 13 2023 *)
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PROG
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(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1] + 1) - prod(i = 1, #f~, if(f[i, 2] == 1, 1, f[i, 1] + 1)); } \\ Amiram Eldar, Oct 13 2023
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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