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

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

Author

Paolo P. Lava, Apr 27 2012

Keywords

• nonn
• nice

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

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

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