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A243348
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Difference between the n-th squarefree number and n: a(n) = A005117(n) - n.
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7
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0, 0, 0, 1, 1, 1, 3, 3, 4, 4, 4, 5, 6, 7, 7, 7, 9, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 16, 16, 19, 20, 21, 22, 22, 22, 23, 23, 25, 25, 25, 26, 26, 26, 27, 27, 29, 29, 29, 31, 31, 32, 32, 32, 33, 34, 35, 35, 35, 36, 39, 39, 39, 40, 40, 40, 41, 41, 41, 42, 42, 42
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OFFSET
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1,7
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COMMENTS
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a(n) <= n, as A243351(n) = 2n - A005117(n) goes never negative (please see the plot A005117(n)/n given in the links section).
No runs longer than three appear, because there must be at least one gap (cf. A053806) in each range [4k+1 .. 4(k+1)] where no term(s) of A005117 appear.
See also A120992 which gives the run lengths.
Record values of first differences: a(2) - a(1) = 0, a(4) - a(3) = 1, a(7) - a(6) = 2, a(32) - a(31) = 3, a(151) - a(150) = 4, a(516) - a(515) = 5, a(13392) - a(13391) = 6, a(131965) - a(131964) = 7, a(664314) - a(664313) = 8, a(5392319) - a(5392318) = 9, and a(134453712) - a(134453711) = 11. - Charles R Greathouse IV, Nov 05 2017
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LINKS
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FORMULA
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PROG
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(PARI) do(x)=my(v=List([0])); forfactored(n=2, x\1, if(vecmax(n[2][, 2])==1, listput(v, n[1]-#v-1))); Vec(v) \\ Charles R Greathouse IV, Nov 05 2017
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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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