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

1,1

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

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)

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][[1]]

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: A000372 A333445 A123930 * A125601 A292811 A025239

Adjacent sequences: A238892 A238893 A238894 * A238896 A238897 A238898

Keyword

nonn

Author

T. D. Noe, Mar 10 2014

Status

approved