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A145899 Numbers n such that sigma(x) = n has more solutions x than any smaller n.

%I A145899 #25 Aug 30 2015 04:07:23
%S A145899 1,12,24,72,168,240,336,360,504,576,720,1440,2880,4320,5760,8640,
%T A145899 10080,15120,17280,20160,30240,40320,60480,120960,181440,241920,
%U A145899 362880,483840,604800,725760,1088640,1209600,1451520,2177280,2419200,2903040,3628800
%N A145899 Numbers n such that sigma(x) = n has more solutions x than any smaller n.
%C A145899 Sequence A206027 has the number of solutions.
%H A145899 Donovan Johnson, <a href="/A145899/b145899.txt">Table of n, a(n) for n = 1..100</a>
%e A145899 sigma(m)=1 has only one solution: m=1.
%e A145899 sigma(m)=12 has two solutions, m=6 and m=11; 12 is the smallest number with more than one such solutions.
%e A145899 sigma(m)=24 has three solutions, m=14,m=15 and m=23; 24 is the smallest number with more than two such solutions.
%e A145899 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.
%t A145899 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 *)
%o A145899 (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
%Y A145899 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).
%Y A145899 Cf. A206027.
%Y A145899 Cf. Untouchable numbers (A005114), sigma-untouchable numbers (A007369) and highly touchable numbers (A238895).
%K A145899 nonn
%O A145899 1,2
%A A145899 _Douglas E. Iannucci_, Oct 22 2008
%E A145899 Extended beyond a(15) by _Klaus Brockhaus_, Oct 27 2008