The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A339940 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A339940

Primitive coreful abundant numbers: coreful abundant numbers having no coreful abundant aliquot divisor.
(history; published version)

#11 by Joerg Arndt at Thu Dec 24 04:47:40 EST 2020

STATUS

reviewed

approved

#10 by Michel Marcus at Thu Dec 24 03:50:12 EST 2020

STATUS

proposed

reviewed

#9 by Amiram Eldar at Thu Dec 24 03:13:30 EST 2020

STATUS

editing

proposed

#8 by Amiram Eldar at Thu Dec 24 02:42:53 EST 2020

LINKS

Amiram Eldar, <a href="/A339940/b339940.txt">Table of n, a(n) for n = 1..1000</a>

STATUS

approved

editing

#7 by N. J. A. Sloane at Wed Dec 23 17:24:59 EST 2020

STATUS

proposed

approved

#6 by Amiram Eldar at Wed Dec 23 17:08:42 EST 2020

STATUS

editing

proposed

#5 by Amiram Eldar at Wed Dec 23 16:08:42 EST 2020

CROSSREFS

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

#4 by Amiram Eldar at Wed Dec 23 16:03:13 EST 2020

CROSSREFS

Cf. A057723, A091191, A307958, A307959, A308053.

#3 by Amiram Eldar at Wed Dec 23 15:55:15 EST 2020

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]

#2 by Amiram Eldar at Wed Dec 23 15:55:01 EST 2020

NAME

allocated for Amiram EldarPrimitive coreful abundant numbers: coreful abundant numbers having no coreful abundant aliquot divisor.

DATA

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.

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, A307958, A307959, A308053.

KEYWORD

allocated

nonn

AUTHOR

Amiram Eldar, Dec 23 2020

STATUS

approved

editing