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

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

Author

Ant King, Apr 17 2007

Keywords

• easy
• nonn

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.

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein, Unitary Divisor.

Crossrefs

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

Programs

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 *)

Formula

The complement of A129485 and A112643.

Extensions

More terms from Amiram Eldar, May 13 2019