Revision History for A181487
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
| older changes
|
| |
| |
| |
|
|
#13 by Alois P. Heinz at Sat Jan 06 19:00:50 EST 2024
| |
| |
| |
|
|
#12 by Andrew Howroyd at Sat Jan 06 18:21:27 EST 2024
| |
| |
| |
|
|
#11 by Andrew Howroyd at Sat Jan 06 15:49:31 EST 2024
|
|
| LINKS
|
WikiepdiaWikipedia, <a href="https://en.wikipedia.org/wiki/Granville_number">Granville number</a>.
|
|
| STATUS
|
approved
editing
|
| |
| |
|
|
#10 by N. J. A. Sloane at Sat Aug 12 00:48:10 EDT 2023
| |
| |
| |
|
|
#9 by Amiram Eldar at Fri Aug 11 03:17:11 EDT 2023
| |
| |
| |
|
|
#8 by Amiram Eldar at Fri Aug 11 02:44:31 EDT 2023
|
|
| COMMENTS
|
Sometimes called S-abundant numbers, since they are analogous to abundant numbers (A005101) as S-perfect numbers (118372A118372) are analogous to perfect numbers (A000396).
|
| |
| |
|
|
#7 by Amiram Eldar at Fri Aug 11 02:44:20 EDT 2023
| |
| |
| |
|
|
#6 by Amiram Eldar at Fri Aug 11 02:43:11 EDT 2023
|
|
| NAME
|
Numbers k such that n < sum( d : Sum_{d|nk, d<nk, d not occurring before ).} d > k.
|
|
| COMMENTS
|
From Amiram Eldar, Aug 11 2023: (Start)
Sometimes called S-abundant numbers, since they are analogous to abundant numbers (A005101) as S-perfect numbers (118372) are analogous to perfect numbers (A000396).
De Koninck and Ivić conjectured that this sequence has an asymptotic density.
The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 15, 152, 1567, 15336, 154301, 1541445, 15392073, ... . Apparently, the asymptotic density of this sequence exists and equals 0.15... . (End)
|
|
| REFERENCES
|
Elena Deza, Perfect and Amicable Numbers, World Scientific, 2023, pp. 325-327.
|
|
| LINKS
|
Jean-Marie De Koninck and Aleksandar Ivić, <a href="https://www.emis.de/journals/PIMB/078/2.html">On a sum of divisors problem</a>, Publications de l'Institut Mathématique (Beograd), New Series, Vol. 64 (78) (1998), pp. 9-20.
Gérard Villemin, <a href="http://villemin.gerard.free.fr/aNombre/TYPDIVIS/ParfaitS.htm">Nombres S-PARFAITS ou Nombres de Granville</a>, NOMBRES - Curiosités, théorie et usages, 2019 (in French).
Wikiepdia, <a href="https://en.wikipedia.org/wiki/Granville_number">Granville number</a>.
|
|
| MATHEMATICA
|
seq[kmax_] := Module[{s = {1}, a = {}, sum}, Do[sum = Total[Select[Divisors[k], MemberQ[s, #] &]]; If[sum <= k, AppendTo[s, k], AppendTo[a, k]], {k, 2, kmax}]; a]; seq[400] (* Amiram Eldar, Aug 11 2023 *)
|
|
| CROSSREFS
|
Cf. A000396, A005101, 118372.
|
|
| STATUS
|
approved
editing
|
| |
| |
|
|
#5 by Joerg Arndt at Sat Sep 14 03:22:22 EDT 2013
| |
| |
| |
|
|
#4 by Donovan Johnson at Sat Sep 14 03:10:41 EDT 2013
| |
| |
| |
|
|
