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%I #43 May 27 2017 05:26:51
%S 1050,1470,1650,1950,3234,3822,8250,9438,9750,11550,13650,16170,17850,
%T 19110,19950,21450,24150,24990,25410,27930,28050,30450,31350,32550,
%U 33150,33810,35490,37050,37950,38850,42042,42630,43050,44850,45150,45570,47190,47850
%N Unitary practical numbers that are nonsquarefree.
%C The squarefree terms of both practical numbers (A005153) and unitary practical numbers (A286652) are the same, A265501.
%H Amiram Eldar, <a href="/A287173/b287173.txt">Table of n, a(n) for n = 1..1000</a>
%t 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]
%Y Cf. A005153, A034448, A265501, A287173, A286652.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 24 2017
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