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A287173 Unitary practical numbers that are nonsquarefree. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 21 23:09 EDT 2021. Contains 348160 sequences. (Running on oeis4.)