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A129486 Odd unitary abundant numbers that are not odd, squarefree, ordinary abundant numbers.

%I A129486 #10 Feb 16 2025 08:33:05
%S A129486 195195,333795,416955,1786785,1996995,2417415,2807805,3138135,3318315,
%T A129486 3708705,3798795,4103715,4339335,4489485,4789785,4967655,5120115,
%U A129486 5420415,5552085,5660655,5731635,6051045,6111105,6263565,6342105,6695535,6771765,6938295,7000455,7088235
%N A129486 Odd unitary abundant numbers that are not odd, squarefree, ordinary abundant numbers.
%C A129486 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 A129486 Amiram Eldar, <a href="/A129486/b129486.txt">Table of n, a(n) for n = 1..10000</a>
%H A129486 Eric Weisstein, <a href="https://mathworld.wolfram.com/UnitaryDivisor.html">Unitary Divisor</a>.
%F A129486 The complement of A129485 and A112643.
%e A129486 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 A129486 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 A129486 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 A129486 Cf. A034683, A129485, A034460, A034448, A129487, A002827, A129468, A112643.
%K A129486 easy,nonn
%O A129486 1,1
%A A129486 _Ant King_, Apr 17 2007
%E A129486 More terms from _Amiram Eldar_, May 13 2019