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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.)