A339940 Primitive coreful abundant numbers: coreful abundant numbers having no coreful abundant aliquot divisor.

72, 108, 200, 784, 900, 1764, 1936, 2704, 2744, 4356, 4900, 6084, 9248, 10404, 11552, 12996, 16928, 19044, 26912, 30276, 34596, 47432, 49284, 60500, 60516, 61504, 66248, 66564, 79524, 84500, 87616, 99225, 101124, 107584, 113288, 118336, 125316, 133956, 141376

Offset: 1

Author

Amiram Eldar, Dec 23 2020

Keywords

• nonn

Comments

Analogous to A091191 as A057723 is analogous to A000203.

All the coreful abundant numbers (A308053) are multiples of terms of this sequence.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A057723, A091191, A302574, A307959, A308053.

Programs

Mathematica

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]