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A073245
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Sum of all cubefree numbers with the same squarefree kernel as the n-th squarefree number.
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2
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1, 6, 12, 30, 72, 56, 180, 132, 182, 336, 360, 306, 380, 672, 792, 552, 1092, 870, 2160, 992, 1584, 1836, 1680, 1406, 2280, 2184, 1722, 4032, 1892, 3312, 2256, 3672, 2862, 3960, 4560, 5220, 3540, 3782, 5952, 5460, 9504, 4556, 6624, 10080, 5112, 5402
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OFFSET
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1,2
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = A062822(n)*A005117(n).
Sum_{n>=1} 1/a(n) = A306633. - Amiram Eldar, Oct 14 2020
a(n) = A064987(A005117(n)). - Michel Marcus, Oct 18 2020
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EXAMPLE
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14 is the 10th squarefree number: A005117(10)=14=2*7, the cubefree numbers with squarefree kernel =14 are 14, 28=2*2*7, 98=2*7*7 and 196=2*2*7*7; therefore a(10)=14+28+98+196=336; a(10)=A062822(10)*A005117(10)=24*14=336.
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MATHEMATICA
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Map[# * DivisorSigma[1, #] &, Select[Range[200], SquareFreeQ]] (* Amiram Eldar, Oct 14 2020 *)
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PROG
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(PARI) apply(x->(x*sigma(x)), select(issquarefree, [1..100])) \\ Michel Marcus, Oct 18 2020
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CROSSREFS
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Cf. A004709, A005117, A007947, A062822, A064987, A072048, A306633.
Sequence in context: A236539 A122211 A015801 * A119626 A152522 A096356
Adjacent sequences: A073242 A073243 A073244 * A073246 A073247 A073248
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Jul 21 2002
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STATUS
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approved
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