A287173 Unitary practical numbers that are nonsquarefree.

1050, 1470, 1650, 1950, 3234, 3822, 8250, 9438, 9750, 11550, 13650, 16170, 17850, 19110, 19950, 21450, 24150, 24990, 25410, 27930, 28050, 30450, 31350, 32550, 33150, 33810, 35490, 37050, 37950, 38850, 42042, 42630, 43050, 44850, 45150, 45570, 47190, 47850

Offset

1,1

Comments

The squarefree terms of both practical numbers (A005153) and unitary practical numbers (A286652) are the same, A265501.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Mathematica

usigma[n_] := Block[{d = Divisors[n]}, Plus @@ Select[d, GCD[ #, n/# ] == 1 &]]; uPracticalQ[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]; r = Sort[p^e]; Do[If[r[[i]] > 1+usigma[prod], ok=False; Break[]]; prod=prod*r[[i]], {i, Length[p]}]; ok]]]; aQ[n_]:=!SquareFreeQ[n]&&uPracticalQ[n]; Select[Range[100000], aQ]

Crossrefs

Cf. A005153, A034448, A265501, A287173, A286652.

Sequence in context: A184203 A015064 A090057 * A204753 A252391 A020389

Adjacent sequences: A287170 A287171 A287172 * A287174 A287175 A287176

Keyword

nonn

Author

Amiram Eldar, May 24 2017

Status

approved