(MAGMAMagma) [n: n in [1..25000000] | not IsSquarefree(9*n+1) and not IsSquarefree(9*n+2) and not IsSquarefree(9*n+3) and not IsSquarefree(9*n+4) and not IsSquarefree(9*n+5) and not IsSquarefree(9*n+6) and not IsSquarefree(9*n+7) and not IsSquarefree(9*n+8)];
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Two of 9n+1..9n+8 are multiples of 4, so concentrate on the other six. The probability that any k of these six are all squarefree is P(k) := Product {p prime > 3} (p^2-k)/p^2. By Inclusioninclusion-Exclusion, exclusion, the probability that none of the six are squarefree is 1 - 6P(1) + 15P(2) - 20P(3) + 15P(4) - 6P(5) + P(6), or roughly one in 92600000. - Michael R Peake, Apr 04 2017
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Two of 9n+1..9n+8 are multiples of 4, so concentrate on the other six. The odds probability that any k of these six are all squarefree is P(k) := Product {p prime > 3} (p^2-k)/p^2. By Inclusion-Exclusion, the odds probability that none of the six are squarefree is 1 - 6P(1) + 15P(2) - 20P(3) + 15P(4) - 6P(5) + P(6), or roughly one in 92600000. - Michael R Peake, Apr 04 2017
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Two of 9n+1..9n+8 are multiples of 4. The proportion of n where , so concentrate on the other six have squares . The odds that any k of these six are all squarefree is between 6!/P(k) := Product {p prime > 3} (5 * 7 * 11 * 13 * 17 * 19p^2-k)/p^2 and (. By Inclusion-Exclusion, the odds that none of the six are squarefree is 1-9/Pi^6P(1)+15P(2)^-20P(3)+15P(4)-6P(5)+P(6), or roughly one in 92600000. - Michael R Peake, Apr 03 04 2017
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Two are multiples of 4. The proportion of n where the other six have squares is between 6!/(5 * 7 * 11 * 13 * 17 * 19)^2 and (1-9/piPi^2)^6 _. - _Michael R Peake_, April Apr 03, 2017
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