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%I #48 Sep 23 2022 07:14:52
%S 2,3,6,21,31,49,73,91,115,121,169,211,301,331,361,391,421,511,631,721,
%T 781,841,1051,1261,1471,1561,1681,1891,2101,2311,2521,2731,3151,3361,
%U 3571,3991,4201,4411,4621,5251,5461,6091,6511,6721,6931,7771,7981,8191,9031
%N Numbers m > 1 such that a record number of numbers k have m as the sum of the proper divisors of k.
%C The number of times that a(n) appears in A001065 is A238896(n).
%C By analogy with the untouchable numbers (A005114) and the highly composite numbers (A002182), these numbers can be named "highly touchable" (see Lignon). - _Daniel Lignon_, Mar 21 2014
%C Indices of record values in A048138. - _Franklin T. Adams-Watters_, Jul 27 2014
%D Daniel Lignon, Dictionnaire de (presque) tous les nombres entiers, Editions Ellipses, 2012, see p. 317 (in French).
%H Amiram Eldar, <a href="/A238895/b238895.txt">Table of n, a(n) for n = 1..245</a> (terms 1..139 from Daniel Mondot)
%e For 2, there are no numbers.
%e For 3, there is 1 number: 4.
%e For 6, there are 2 numbers: 6 and 25.
%e For 21, there are 3 numbers: 18, 51, 91.
%e For 31, there are 5 numbers: 32, 125, 161, 209, 221.
%e For 49, there are 6 numbers: 75, 215, 287, 407, 527, 551.
%t nn = 1000; s = Table[0, {nn}]; Do[k = DivisorSigma[1, n] - n; If[0 < k <= nn, s[[k]]++], {n, nn^2}]; t = {}; mx = -1; Do[If[s[[n]] > mx, mx = s[[n]]; AppendTo[t, {n, mx}]], {n, 2, nn}]; Transpose[t][[1]]
%Y Cf. A001065, A005114, A048138, A238896.
%Y Cf. A152454 (row n lists the numbers whose proper divisors sum to n).
%Y Cf. A239625 (irregular table giving the rows of numbers that produce a(n)).
%K nonn
%O 1,1
%A _T. D. Noe_, Mar 10 2014
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