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A339940
Primitive coreful abundant numbers: coreful abundant numbers having no coreful abundant aliquot divisor.
4
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Dec 23 2020
STATUS
approved