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 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]][] > mn, mn = t2[[n]][]; AppendTo[t3, t2[[n]][]]], {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

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