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

1,2

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