A218981 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.

5, 9, 14, 15, 20, 21, 22, 25, 26, 27, 28, 32, 33, 34, 35, 38, 39, 40, 42, 44, 45, 46, 49, 50, 51, 52, 54, 55, 56, 57, 58, 62, 63, 64, 65, 66, 68, 69, 70, 74, 75, 76, 77, 78, 80, 81, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 98, 99, 100

Offset: 1

Author

Jon Perry, Nov 08 2012

Keywords

• nonn

Comments

Conjecture: This sequence is infinite.

Examples

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

Crossrefs

Cf. A000203, A211223, A218852, A218980.

Programs

JavaScript

function divisorSum(n) {
c=0;
for (i=1;i<=n;i++) if (n%i==0) c+=i;
return c;
}
ds=new Array();
for (j=1;j<401;j++) ds[j]=divisorSum(j);
a=new Array();
ac=0;
for (j=1;j<100;j++)
for (k=1;k<=j;k++)
for (m=1;m<=k;m++)
for (n=1;n<=m;n++)
if (ds[j]+ds[k]+ds[m]+ds[n]==ds[j+k+m+n]) a[ac++]=j+k+m+n;
a.sort(function(a, b) {return a-b;});
i=0;
while(i++