

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
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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), sigmauntouchable 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



