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

1,1

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

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]

Crossrefs

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

Sequence in context: A114128 A143610 A166987 * A251124 A169644 A078667

Adjacent sequences: A339937 A339938 A339939 * A339941 A339942 A339943

Keyword

nonn

Author

Amiram Eldar, Dec 23 2020

Status

approved