A302574 Primitive unitary abundant numbers (definition 2): unitary abundant numbers (A034683) having no unitary abundant proper unitary divisor.

30, 42, 66, 70, 78, 102, 114, 138, 150, 174, 186, 222, 246, 258, 282, 294, 318, 354, 366, 402, 420, 426, 438, 474, 498, 534, 582, 606, 618, 642, 654, 660, 678, 726, 750, 762, 780, 786, 822, 834, 840, 894, 906, 924, 942, 978, 990, 1002, 1014, 1020, 1038, 1074

Offset: 1

Author

Amiram Eldar, Apr 10 2018

Keywords

• nonn

Comments

The unitary analog of A091191.

Examples

			70 is primitive unitary abundant since it is unitary abundant (usigma(70) = 144 > 2*70), and all of its unitary divisors are unitary deficient. 210 is unitary abundant since usigma(210) = 576 > 2*210, but is not in this sequence since 70 is one of its unitary divisors, and 70 is unitary abundant.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A034448, A034683, A091191, A129487, A302573.

Programs

Mathematica

usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; delta[n_] := usigma[n]-2n; udefQ[n_] := Module[{}, v=Most[Module[{d = Divisors[n]}, Select[ d, GCD[ #, n/# ] == 1 &]]]; u = Max[Map[delta,v]]; u<=0 ]; puaQ[n_] := delta[n] > 0 && udefQ[n]; Select[Range[10000],puaQ]