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 A268156 Smallest squarefree term of adjacent squarefree pairs in the sequence of practical numbers (A005153). 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Wikipedia, Practical number Wikipedia, Squarefree integer EXAMPLE 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. MATHEMATICA 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 CROSSREFS Cf. A005117, A005153, A265501. Sequence in context: A174753 A031557 A031737 * A180994 A204721 A204960 Adjacent sequences: A268153 A268154 A268155 * A268157 A268158 A268159 KEYWORD nonn AUTHOR Frank M Jackson, Jan 27 2016 STATUS approved

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Last modified March 26 02:36 EDT 2023. Contains 361529 sequences. (Running on oeis4.)