A238895 Numbers m > 1 such that a record number of numbers k have m as the sum of the proper divisors of k.

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

Offset: 1

Author

T. D. Noe, Mar 10 2014

Keywords

• nonn

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

Examples

			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.
		

References

• Daniel Lignon, Dictionnaire de (presque) tous les nombres entiers, Editions Ellipses, 2012, see p. 317 (in French).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..245 (terms 1..139 from Daniel Mondot)

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)).

Programs

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][[1]]