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A268156
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Smallest squarefree term of adjacent squarefree pairs in the sequence of practical numbers (A005153).
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2
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1, 3486, 41106, 50358, 77142, 102090, 104610, 118734, 119910, 142662, 155298, 159654, 173910, 192210, 193290, 203010, 205062, 212898, 220818, 228018, 232518, 238170, 239946, 241878, 254478, 265278, 266178, 272118, 273378, 303630, 306210, 311178, 323778, 326370, 331890, 335478, 335946, 336102
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OFFSET
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1,2
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COMMENTS
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The first occurrence of adjacent squarefree practical number pairs is 1, 2.
The first occurrence of adjacent squarefree practical number triples is 792834, 792858, 792870.
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..10000
Wikipedia, Practical number
Wikipedia, Squarefree integer
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EXAMPLE
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a(2) = 3486 = 2*3*7*83 and is squarefree. The next practical number is 3498 = 2*3*11*53 and is also squarefree. This is the second such pairing.
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MATHEMATICA
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PracticalQ[n_] := Module[{f, p, e, prod=1, ok=True}, If[n<1||(n>1&&OddQ[n]), False, If[n==1, True, f=FactorInteger[n]; {p, e}=Transpose[f]; Do[If[p[[i]]>1+DivisorSigma[1, prod], ok=False; Break[]]; prod=prod*p[[i]]^e[[i]], {i, Length[p]}]; ok]]]; lst=Select[Range[1000000], PracticalQ]; lst1={}; Do[If[SquareFreeQ[lst[[n]]]&&SquareFreeQ[lst[[n+1]]], AppendTo[lst1, lst[[n]]]], {n, 1, Length[lst]-1}]; lst1
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CROSSREFS
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Cf. A005117, A005153, A265501.
Sequence in context: A174753 A031557 A031737 * A180994 A204721 A204960
Adjacent sequences: A268153 A268154 A268155 * A268157 A268158 A268159
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KEYWORD
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nonn
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AUTHOR
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Frank M Jackson, Jan 27 2016
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STATUS
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approved
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