A357696 Cubefree primitive abundant numbers: cubefree abundant numbers having no abundant proper divisor.

12, 18, 20, 30, 42, 66, 70, 78, 102, 114, 138, 174, 186, 196, 222, 246, 258, 282, 308, 318, 354, 364, 366, 402, 426, 438, 474, 476, 498, 532, 534, 550, 572, 582, 606, 618, 642, 644, 650, 654, 678, 748, 762, 786, 812, 822, 834, 836, 868, 894, 906, 942, 978, 1002

Offset

1,1

Links

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

Mathematica

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[#] &]

Prog

(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};

Crossrefs

Intersection of A004709 and A091191.

Subsequence of A357695.

A249242 is a subsequence.

Cf. A308618.

Sequence in context: A192819 A181487 A091191 * A259980 A257719 A071927

Adjacent sequences: A357693 A357694 A357695 * A357697 A357698 A357699

Keyword

nonn

Author

Amiram Eldar, Oct 10 2022

Status

approved