A247131 Numbers n > 0 such that a record number of composite numbers k have n as the sum of the nontrivial divisors of k.

1, 2, 5, 20, 30, 48, 72, 90, 114, 120, 168, 210, 300, 330, 360, 390, 420, 510, 630, 720, 780, 840, 1050, 1260, 1470, 1560, 1680, 1890, 2100, 2310, 2520, 2730, 3150, 3360, 3570, 3990, 4200, 4410, 4620, 5250, 5460, 6090, 6510, 6720, 6930, 7770, 7980, 8190, 9030, 9240, 10710, 10920, 11550, 13020, 13650, 13860, 15540

Offset

1,2

Comments

A prime number has no nontrivial divisors so their sum is = 0. That's why we take only composite numbers.

Links

Amiram Eldar, Table of n, a(n) for n = 1..139

Formula

Obviously a(n) = A238895(n)-1.

Example

For 1, there are no numbers.
For 2, there is 1 number: 4.
For 5, there are 2 numbers: 6 and 25.
For 20, there are 3 numbers: 18, 51, 91.

Mathematica

ch[1] = 0; ch[n_] := DivisorSigma[1, n] - n - 1; m = 300; v = Table[0, {m}]; Do[c = ch[k]; If[1 <= c <= m, v[[c]]++], {k, 1, m^2}]; s = {}; vm = -1; Do[If[v[[k]] > vm, vm = v[[k]]; AppendTo[s, k]], {k, 1, m}]; s (* Amiram Eldar, Nov 05 2019 *)

Crossrefs

Cf. A145899 (similar but with all divisors), A238895 (similar but with proper divisors), A048050 (Chowla's function: sum of nontrivial divisors).

Sequence in context: A136900 A136898 A077138 * A192164 A244087 A361134

Adjacent sequences: A247128 A247129 A247130 * A247132 A247133 A247134

Keyword

nonn

Author

Daniel Lignon, Nov 22 2014

Status

approved