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Odd unitary abundant numbers that are not odd, squarefree, ordinary abundant numbers.
3

%I #9 May 13 2019 05:52:04

%S 195195,333795,416955,1786785,1996995,2417415,2807805,3138135,3318315,

%T 3708705,3798795,4103715,4339335,4489485,4789785,4967655,5120115,

%U 5420415,5552085,5660655,5731635,6051045,6111105,6263565,6342105,6695535,6771765,6938295,7000455,7088235

%N Odd unitary abundant numbers that are not odd, squarefree, ordinary abundant numbers.

%C The first 50 members of A129485 and A112643 are the same. However, the sequences differ thereafter and this sequence contains those integers that are included in A129485 but are not included in A112643.

%H Amiram Eldar, <a href="/A129486/b129486.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein, <a href="http://mathworld.wolfram.com/UnitaryDivisor.html">Unitary Divisor</a>.

%F The complement of A129485 and A112643.

%e The third integer which is an odd unitary abundant number but is not an ordinary, squarefree abundant number is 416955. Hence a(3)=416955.

%t UnitaryDivisors[ n_Integer?Positive ] := Select[ Divisors[ n ], GCD[ #, n/# ] == 1 & ]; sstar[ n_ ] := Plus @@ UnitaryDivisors[ n ] - n; UnitaryAbundantNumberQ[ k_ ] := If[ sstar[ k ] > k, True, False ]; data1 = Select[ Range[ 1, 10^7, 2 ], UnitaryAbundantNumberQ[ # ] & ]; data2 = Select[ Range[ 1, 10^7, 2 ], DivisorSigma[ 1, # ] - 2 # > 0 && ! MoebiusMu[ # ] == 0 & ]; Complement[ data1, data2 ]

%t uaQ[n_] := Module[{f = FactorInteger[n]}, Max[f[[;;,2]]] > 1 && Times@@(1 + Power @@@ f) > 2n]; Select[Range[3, 2*10^6, 2], uaQ] (* _Amiram Eldar_, May 13 2019 *)

%Y Cf. A034683, A129485, A034460, A034448, A129487, A002827, A129468, A112643.

%K easy,nonn

%O 1,1

%A _Ant King_, Apr 17 2007

%E More terms from _Amiram Eldar_, May 13 2019