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

Author

Daniel Lignon, Nov 22 2014

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)

Formula

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