

A302574


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


3



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
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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



