OFFSET
1,1
COMMENTS
Conjecture: This sequence is infinite.
EXAMPLE
1 + 1 + 3 + 4 = 9 and sigma(1) + sigma(1) + sigma(3) + sigma(4) = 1 + 1 + 4 + 7 = 13 = sigma(9).
PROG
(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++<a.length-1)
if (a[i]==a[i+1]) a.splice(i--, 1);
document.writeln(a);
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon Perry, Nov 08 2012
STATUS
approved