login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A145899 Numbers n such that sigma(x) = n has more solutions x than any smaller n. 10
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; text; 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, ", ")))} \\ Klaus Brockhaus, 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).

Cf. A206027.

Cf. Untouchable numbers (A005114), sigma-untouchable numbers (A007369) and highly touchable numbers (A238895).

Sequence in context: A332039 A001335 A206026 * A172011 A239635 A001041

Adjacent sequences:  A145896 A145897 A145898 * A145900 A145901 A145902

KEYWORD

nonn

AUTHOR

Douglas E. Iannucci, Oct 22 2008

EXTENSIONS

Extended beyond a(15) by Klaus Brockhaus, Oct 27 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 4 09:03 EDT 2020. Contains 336201 sequences. (Running on oeis4.)