|
| |
|
|
A034090
|
|
Numbers whose sum of proper divisors exceeds that of all smaller numbers.
|
|
14
|
|
|
|
1, 2, 4, 6, 8, 10, 12, 18, 20, 24, 30, 36, 48, 60, 72, 84, 90, 96, 108, 120, 144, 168, 180, 216, 240, 288, 300, 336, 360, 420, 480, 504, 540, 600, 660, 720, 840, 960, 1008, 1080, 1200, 1260, 1440, 1560, 1680, 1980, 2100, 2160, 2340, 2400, 2520, 2880, 3120, 3240
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
The highly abundant numbers A002093 are a subsequence since if sigma(k) - k > sigma(m) - m for all m < n then sigma(k) > sigma(m). - Charles R Greathouse IV, Sep 13 2016
|
|
|
LINKS
|
Robert G. Wilson v, Table of n, a(n) for n = 1..2750 (first 372 terms from T. D. Noe, terms 373 to 1000 from Donovan Johnson)
|
|
|
EXAMPLE
|
From William A. Tedeschi, Aug 19 2010: (Start)
-- 12: 1+2+3+4+6 = 16
13: 1 = 1
14: 1+2+7 = 10
15: 1+3+5 = 9
16: 1+2+4+8 = 15
17: 1 = 1
-- 18: 1+2+3+6+9 = 21
As 12 had the previous (earliest) highest, it is a term; then since 18 has the new highest, it is a term. (End)
|
|
|
MATHEMATICA
|
A = {}; mx = -1; For[ k = 1, k < 10000, k++, t = DivisorSigma[1, k] - k; If[ t > mx, mx = t; AppendTo[A, k]]]; A (* slightly modified by Robert G. Wilson v, Aug 28 2022 *)
|
|
|
PROG
|
(PARI) r=0; for(n=1, 1e6, t=sigma(n)-n; if(t>r, r=t; print1(n", "))) \\ Charles R Greathouse IV, Sep 13 2016
|
|
|
CROSSREFS
|
Supersequence of A002093.
Cf. A001065, A034091, A034287, A034288.
Sequence in context: A100180 A258137 A101814 * A146344 A162763 A113242
Adjacent sequences: A034087 A034088 A034089 * A034091 A034092 A034093
|
|
|
KEYWORD
|
nonn,nice
|
|
|
AUTHOR
|
J. Lowell
|
|
|
EXTENSIONS
|
More terms from Erich Friedman
|
|
|
STATUS
|
approved
|
| |
|
|
