|
| |
|
|
A145899
|
|
Numbers n such that sigma(x) = n has more solutions x than any smaller n.
|
|
3
| |
|
|
1, 12, 24, 72, 168, 240, 336, 360, 504, 576, 720, 1440, 2880, 4320, 5760, 8640, 10080, 15120, 17280, 20160, 30240, 40320, 60480, 120960, 181440, 241920, 362880, 483840, 604800, 725760, 1088640, 1209600, 1451520, 2177280, 2419200, 2903040, 3628800
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Sequence A206027 has the number of solutions.
|
|
|
LINKS
| Donovan Johnson, Table of n, a(n) for n = 1..100
|
|
|
EXAMPLE
| sigma(m)=1 has only one solution: m=1.
sigma(m)=12 has two solutions, m=6 and m=11; 12 is the smallest number with more than one such solutions.
sigma(m)=24 has three solutions, m=14,m=15 and m=23; 24 is the smallest number with more than two such solutions.
sigma(m)=72 has five solutions, m=30, m=46, m=51, m=55 and m=71; 72 is the smallest number with more than three such solutions.
|
|
|
MATHEMATICA
| t = DivisorSigma[1, Range[10^6]]; t2 = Sort[Tally[t]]; mn = 0; t3 = {}; Do[If[t2[[n]][[2]] > mn, mn = t2[[n]][[2]]; AppendTo[t3, t2[[n]][[1]]]], {n, Length[t2]}]; t3 (* T. D. Noe, Feb 03 2012 *)
|
|
|
PROG
| (PARI) {m=3650000; v=vectorsmall(m); for(n=1, m, s=sigma(n); if(s<=m, v[s]++)); g=0; j=1; while(j<=m, if(v[j]<=g, j++, g=v[j]; print1(j, ", ")))} [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 27 2008]
|
|
|
CROSSREFS
| Cf. A000203 (sum of divisors of n), A054973 (number of numbers whose divisors sum to n), A007368 (smallest k such that sigma(x) = k has exactly n solutions).
Sequence in context: A063975 A001335 A206026 * A172011 A001041 A081751
Adjacent sequences: A145896 A145897 A145898 * A145900 A145901 A145902
|
|
|
KEYWORD
| nonn,changed
|
|
|
AUTHOR
| Douglas E. Iannucci (diannuc(AT)uvi.edu), Oct 22 2008
|
|
|
EXTENSIONS
| Extended beyond a(15) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 27 2008
|
| |
|
|
