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

Author

Amiram Eldar, May 24 2017

Keywords

• nonn

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

Crossrefs

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

Programs

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]