A268156 Smallest squarefree term of adjacent squarefree pairs in the sequence of practical numbers (A005153).

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

Offset: 1

Author

Frank M Jackson, Jan 27 2016

Keywords

• nonn

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.

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Wikipedia, Practical number
• Wikipedia, Squarefree integer

Crossrefs

Cf. A005117, A005153, A265501.

Programs

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