A302574 - OEIS

%I #9 Jun 22 2019 19:02:04

%S 30,42,66,70,78,102,114,138,150,174,186,222,246,258,282,294,318,354,

%T 366,402,420,426,438,474,498,534,582,606,618,642,654,660,678,726,750,

%U 762,780,786,822,834,840,894,906,924,942,978,990,1002,1014,1020,1038,1074

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

%C The unitary analog of A091191.

%H Amiram Eldar, <a href="/A302574/b302574.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%t 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]

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

%K nonn

%O 1,1

%A _Amiram Eldar_, Apr 10 2018