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A070284
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Smallest of 4 consecutive numbers each divisible by a square.
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12
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242, 844, 845, 1680, 1681, 2888, 2889, 3174, 3624, 3625, 3750, 5046, 5047, 8475, 8523, 8954, 10050, 10827, 10924, 10925, 11322, 13374, 14748, 14749, 15775, 15848, 15849, 16575, 17404, 17405, 19647, 19940, 19941, 20574, 21462
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OFFSET
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1,1
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COMMENTS
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This sequence has positive density in N; the density is around 0.0025.
The sequence includes an infinite family of arithmetic progressions. Such AP's can be constructed to each term, with large differences [like e.g. square of primorials, A061742]. It is necessary to solve suitable systems of linear Diophantine equations. E.g.: subsequences of quadruples of terms = {44100k+29349, 44100k+29350, 44100k+29351, 44100+29352} = {9(49000k+3261, 25(1764k+1174), 49(900k+599), 4(11025k+7338)}; starting terms in this sequence = {29349, 73449, 117649...}; difference = A002110(4)^2 = 2310^2. - Labos Elemer, Nov 25 2002
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LINKS
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FORMULA
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MATHEMATICA
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f[n_] := Union[Transpose[FactorInteger[n]][[2]]][[ -1]]; a = 0; b = 1; c = 0; Do[d = f[n]; If[a > 1 && b > 1 && c > 1 && d > 1, Print[n - 3]]; a = b; b = c; c = d, {n, 4, 10^6}]
Flatten[Position[Partition[SquareFreeQ/@Range[60000], 4, 1], _?(Union[#] == {False}&), {1}, Heads->False]] (* Harvey P. Dale, May 24 2014 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Sharon Sela (sharonsela(AT)hotmail.com), May 09 2002
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EXTENSIONS
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STATUS
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approved
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