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%I #11 Dec 24 2020 04:47:40
%S 72,108,200,784,900,1764,1936,2704,2744,4356,4900,6084,9248,10404,
%T 11552,12996,16928,19044,26912,30276,34596,47432,49284,60500,60516,
%U 61504,66248,66564,79524,84500,87616,99225,101124,107584,113288,118336,125316,133956,141376
%N Primitive coreful abundant numbers: coreful abundant numbers having no coreful abundant aliquot divisor.
%C Analogous to A091191 as A057723 is analogous to A000203.
%C All the coreful abundant numbers (A308053) are multiples of terms of this sequence.
%H Amiram Eldar, <a href="/A339940/b339940.txt">Table of n, a(n) for n = 1..1000</a>
%t f[p_, e_] := (p^(e + 1) - 1)/(p - 1) - 1; s[1] = 1; s[n_] := Times @@ (f @@@ FactorInteger[n]); cabQ[n_] := s[n] > 2*n; pricabQ[n_] := cabQ[n] && AllTrue[Most @ Divisors[n], !cabQ[#] &]; Select[Range[10^5], pricabQ]
%Y Cf. A057723, A091191, A302574, A307959, A308053.
%K nonn
%O 1,1
%A _Amiram Eldar_, Dec 23 2020
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