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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 (list; graph; refs; listen; history; text; internal format)
 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 Amiram Eldar, Table of n, a(n) for n = 1..10000 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 *) CROSSREFS Cf. A034683, A129485, A034460, A034448, A129487, A002827, A129468, A112643. Sequence in context: A172790 A247132 A069305 * A203047 A309190 A074388 Adjacent sequences:  A129483 A129484 A129485 * A129487 A129488 A129489 KEYWORD easy,nonn AUTHOR Ant King, Apr 17 2007 EXTENSIONS More terms from Amiram Eldar, May 13 2019 STATUS approved

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Last modified April 13 06:52 EDT 2021. Contains 342935 sequences. (Running on oeis4.)