A357696 - OEIS

%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