

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



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
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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



FORMULA



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).


KEYWORD

nonn


AUTHOR



STATUS

approved



