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 A238895 Numbers n > 1 such that a record number of numbers k have n as the sum of the proper divisors of k. 8
 2, 3, 6, 21, 31, 49, 73, 91, 115, 121, 169, 211, 301, 331, 361, 391, 421, 511, 631, 721, 781, 841, 1051, 1261, 1471, 1561, 1681, 1891, 2101, 2311, 2521, 2731, 3151, 3361, 3571, 3991, 4201, 4411, 4621, 5251, 5461, 6091, 6511, 6721, 6931, 7771, 7981, 8191, 9031 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The number of times that a(n) appears in A001065 is A238896(n). 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 Indices of record values in A048138. - Franklin T. Adams-Watters, Jul 27 2014 REFERENCES D. Lignon, Dictionnaire de (presque) tous les nombres entiers, Editions Ellipses, 2012, see p. 317 (in French). LINKS Daniel Mondot, Table of n, a(n) for n = 1..139 EXAMPLE For 2, there are no numbers. For 3, there is 1 number: 4. For 6, there are 2 numbers: 6 and 25. For 21, there are 3 numbers: 18, 51, 91. For 31, there are 5 numbers: 32, 125, 161, 209, 221. For 49, there are 6 numbers: 75, 215, 287, 407, 527, 551. MATHEMATICA 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][] CROSSREFS Cf. A001065, A005114, A048138, A238896. Cf. A152454 (row n lists the numbers whose proper divisors sum to n). Cf. A239625 (irregular table giving the rows of numbers that produce a(n)). Sequence in context: A002078 A000372 A123930 * A125601 A292811 A025239 Adjacent sequences:  A238892 A238893 A238894 * A238896 A238897 A238898 KEYWORD nonn AUTHOR T. D. Noe, Mar 10 2014 STATUS approved

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)