%I #9 Oct 12 2022 04:12:18
%S 12,18,20,30,42,66,70,78,102,114,138,174,186,196,222,246,258,282,308,
%T 318,354,364,366,402,426,438,474,476,498,532,534,550,572,582,606,618,
%U 642,644,650,654,678,748,762,786,812,822,834,836,868,894,906,942,978,1002
%N Cubefree primitive abundant numbers: cubefree abundant numbers having no abundant proper divisor.
%H Amiram Eldar, <a href="/A357696/b357696.txt">Table of n, a(n) for n = 1..10000</a>
%t cubeFreeQ[n_] := Max[FactorInteger[n][[;; , 2]]] < 3; primQ[n_] := DivisorSigma[-1, n] > 2 && AllTrue[n/FactorInteger[n][[;; , 1]], DivisorSigma[-1, #] <= 2 &]; Select[Range[1500], cubeFreeQ[#] && primQ[#] &]
%o (PARI) is(n) = {my(f = factor(n)); for(i = 1, #f~, if(f[i, 2] > 2, return(0))); if(sigma(f, -1) <= 2, return(0)); for(i = 1, #f~, if(sigma(n/f[i,1], -1) > 2, return(0))); 1};
%Y Intersection of A004709 and A091191.
%Y Subsequence of A357695.
%Y A249242 is a subsequence.
%Y Cf. A308618.
%K nonn
%O 1,1
%A _Amiram Eldar_, Oct 10 2022