A268156 - OEIS

%I #12 Oct 21 2019 11:23:54

%S 1,3486,41106,50358,77142,102090,104610,118734,119910,142662,155298,

%T 159654,173910,192210,193290,203010,205062,212898,220818,228018,

%U 232518,238170,239946,241878,254478,265278,266178,272118,273378,303630,306210,311178,323778,326370,331890,335478,335946,336102

%N Smallest squarefree term of adjacent squarefree pairs in the sequence of practical numbers (A005153).

%C The first occurrence of adjacent squarefree practical number pairs is 1, 2.

%C The first occurrence of adjacent squarefree practical number triples is 792834, 792858, 792870.

%H Amiram Eldar, <a href="/A268156/b268156.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Practical_number">Practical number</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Squarefree_integer">Squarefree integer</a>

%e 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.

%t 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

%Y Cf. A005117, A005153, A265501.

%K nonn

%O 1,2

%A _Frank M Jackson_, Jan 27 2016