cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A218980 Integers not in A218852.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 9, 11, 12, 17, 18, 22, 23, 24, 29, 30, 36, 37, 41, 47, 48, 53, 59, 60, 67, 71, 72, 79, 83, 89, 97, 101, 107, 113, 120, 127, 131, 137, 144, 149, 157, 163, 167, 173, 179, 180, 191, 197, 210, 211, 223, 227, 233, 239, 240, 251, 257, 263, 269, 277
Offset: 1

Views

Author

Jon Perry, Nov 08 2012

Keywords

Comments

Conjecture: This sequence is infinite.

Crossrefs

Cf. A218852.

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<1001;j++) ds[j]=divisorSum(j);
a=new Array();
ac=0;
for (j=1;j<300;j++)
for (k=1;k<=j;k++)
for (m=1;m<=k;m++)
if (ds[j]+ds[k]+ds[m]==ds[j+k+m]) a[ac++]=j+k+m;
a.sort(function(a, b) {return a-b;});
i=0;
while(i++

A211223 Numbers k for which sigma(k) = sigma(x) + sigma(y), where k = x + y.

Original entry on oeis.org

3, 8, 9, 10, 15, 20, 21, 30, 32, 33, 39, 40, 49, 51, 55, 56, 57, 62, 63, 69, 70, 75, 85, 87, 88, 90, 92, 93, 94, 96, 99, 104, 105, 108, 110, 111, 114, 116, 117, 123, 125, 126, 128, 129, 130, 134, 135, 136, 140, 141, 145, 147, 150, 152, 153, 155, 158, 159, 160
Offset: 1

Views

Author

Paolo P. Lava, Apr 27 2012

Keywords

Comments

A211225(a(n)) > 0. - Reinhard Zumkeller, Jan 06 2013

Examples

			sigma(49) = sigma(8) + sigma(41) that is 57 = 15 + 42.
sigma(93) = sigma(31) + sigma(62) that is 128 = 32 + 96.
In more than one way: sigma(117) = sigma(41) + sigma(76) = sigma(52) + sigma(65) = sigma(56) + sigma(61) that is 182 = 42 + 140 = 98 + 84 = 120 + 62.

Links

Crossrefs

Cf. A083207, A204830, A204831, A211224, A211225.
Cf. A218852.
Cf. A000203.

Programs

  • Haskell
    a211223 n = a211223_list !! (n-1)
a211223_list = map (+ 1) $ findIndices (> 0) a211225_list
-- Reinhard Zumkeller, Jan 06 2013
  • Maple
    with(numtheory);
A211223:=proc(q)
local i,n;
for n from 1 to q do
  for i from 1 to trunc(n/2) do
    if sigma(i)+sigma(n-i)=sigma(n) then print(n); break; fi;
od; od; end:
A211223(10000);
  • Mathematica
    sigmaPartitionQ[n_] := With[{s = DivisorSigma[1, n], ip = IntegerPartitions[ n, {2}]}, MemberQ[ip, {x_, y_} /; s == DivisorSigma[ 1, x] + DivisorSigma[ 1, y]]]; Select[Range[160], sigmaPartitionQ] (* Jean-François Alcover, Aug 19 2013 *)
  • PARI
    is(n)=my(t=sigma(n));for(i=1,n\2,if(sigma(i)+sigma(n-i)==t, return(1))) \\ Charles R Greathouse IV, May 04 2012

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.

Original entry on oeis.org

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

Views

Author

Jon Perry, Nov 08 2012

Keywords

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++
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.