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

1,1

Comments

The unitary analog of A091191.

Links

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

Example

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.

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]

Crossrefs

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

Sequence in context: A306217 A034683 A328328 * A087248 A249242 A189759

Adjacent sequences: A302571 A302572 A302573 * A302575 A302576 A302577

Keyword

nonn

Author

Amiram Eldar, Apr 10 2018

Status

approved