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A129486
Odd unitary abundant numbers that are not odd, squarefree, ordinary abundant numbers.
3
195195, 333795, 416955, 1786785, 1996995, 2417415, 2807805, 3138135, 3318315, 3708705, 3798795, 4103715, 4339335, 4489485, 4789785, 4967655, 5120115, 5420415, 5552085, 5660655, 5731635, 6051045, 6111105, 6263565, 6342105, 6695535, 6771765, 6938295, 7000455, 7088235
OFFSET
1,1
COMMENTS
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.
LINKS
Eric Weisstein, Unitary Divisor.
FORMULA
The complement of A129485 and A112643.
EXAMPLE
The third integer which is an odd unitary abundant number but is not an ordinary, squarefree abundant number is 416955. Hence a(3)=416955.
MATHEMATICA
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 ]
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 *)
KEYWORD
easy,nonn
AUTHOR
Ant King, Apr 17 2007
EXTENSIONS
More terms from Amiram Eldar, May 13 2019
STATUS
approved