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
KEYWORD
nonn
AUTHOR
Frank M Jackson, Jan 27 2016
STATUS
approved