A247131 - OEIS

%I #46 Nov 05 2019 06:55:13

%S 1,2,5,20,30,48,72,90,114,120,168,210,300,330,360,390,420,510,630,720,

%T 780,840,1050,1260,1470,1560,1680,1890,2100,2310,2520,2730,3150,3360,

%U 3570,3990,4200,4410,4620,5250,5460,6090,6510,6720,6930,7770,7980,8190,9030,9240,10710,10920,11550,13020,13650,13860,15540

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

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

%H Amiram Eldar, <a href="/A247131/b247131.txt">Table of n, a(n) for n = 1..139</a>

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

%e For 1, there are no numbers.

%e For 2, there is 1 number: 4.

%e For 5, there are 2 numbers: 6 and 25.

%e For 20, there are 3 numbers: 18, 51, 91.

%t 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 *)

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

%K nonn

%O 1,2

%A _Daniel Lignon_, Nov 22 2014