A218981 - OEIS

%I #12 Dec 07 2019 21:03:59

%S 5,9,14,15,20,21,22,25,26,27,28,32,33,34,35,38,39,40,42,44,45,46,49,

%T 50,51,52,54,55,56,57,58,62,63,64,65,66,68,69,70,74,75,76,77,78,80,81,

%U 82,85,86,87,88,91,92,93,94,95,96,98,99,100

%N Numbers n for which sigma(n) = sigma(w) + sigma(x) + sigma(y) + sigma(z), where n = w + x + y + z, with w, x, y, z all positive.

%C Conjecture: This sequence is infinite.

%e 1 + 1 + 3 + 4 = 9 and sigma(1) + sigma(1) + sigma(3) + sigma(4) = 1 + 1 + 4 + 7 = 13 = sigma(9).

%o (JavaScript)

%o function divisorSum(n) {

%o c=0;

%o for (i=1;i<=n;i++) if (n%i==0) c+=i;

%o return c;

%o }

%o ds=new Array();

%o for (j=1;j<401;j++) ds[j]=divisorSum(j);

%o a=new Array();

%o ac=0;

%o for (j=1;j<100;j++)

%o for (k=1;k<=j;k++)

%o for (m=1;m<=k;m++)

%o for (n=1;n<=m;n++)

%o if (ds[j]+ds[k]+ds[m]+ds[n]==ds[j+k+m+n]) a[ac++]=j+k+m+n;

%o a.sort(function(a, b) {return a-b;});

%o i=0;

%o while(i++<a.length-1)

%o if (a[i]==a[i+1]) a.splice(i--,1);

%o document.writeln(a);

%Y Cf. A000203, A211223, A218852, A218980.

%K nonn

%O 1,1

%A _Jon Perry_, Nov 08 2012