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

1,1

Comments

Conjecture: This sequence is infinite.

Links

Table of n, a(n) for n=1..60.

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

Cf. A000203, A211223, A218852, A218980.

Sequence in context: A061516 A146135 A101116 * A030772 A314799 A288871

Adjacent sequences: A218978 A218979 A218980 * A218982 A218983 A218984

Keyword

nonn

Author

Jon Perry, Nov 08 2012

Status

approved