A211224 Least k with precisely n partitions k = x + y satisfying sigma(k) = sigma(x) + sigma(y).

3, 32, 117, 183, 393, 728, 933, 2193, 2528, 1173, 6136, 2990, 4070, 8211, 11488, 12616, 6112, 22287, 20584, 37468, 38675, 35245, 41416, 55825, 43616, 66385, 56810, 94040, 88736, 93975, 90068, 174515, 169376, 146965, 139196, 210453, 140576, 177248

Offset: 1

Author

Paolo P. Lava, May 04 2012

Keywords

• nonn

Comments

Subset of A211223.

Examples

			a(7)=933; 933 has 7 partitions of two numbers, x and y, for which sigma(933) = sigma(x) + sigma(y) = 1248. In fact:
sigma(311) + sigma(622) = 312 + 936 = 1248;
sigma(322) + sigma(611) = 576 + 672 = 1248;
sigma(370) + sigma(563) = 684 + 564 = 1248;
sigma(391) + sigma(542) = 432 + 816 = 1248;
sigma(398) + sigma(535) = 600 + 648 = 1248;
sigma(407) + sigma(526) = 456 + 792 = 1248;
sigma(442) + sigma(491) = 756 + 492 = 1248;
Furthermore 933 is the minimum number to have this property.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A083207, A204830, A204831, A211223, A211225.

Programs

Maple

with(numtheory);
A211224:=proc(q)
local a,b,i,j,n,v;
v:=array(1..10000); for n from 1 to 10000 do v[n]:=0; od;
a:=0;
for n from 1 to q do
  b:=0;
  for i from 1 to trunc(n/2) do
    if sigma(i)+sigma(n-i)=sigma(n) then b:=b+1; fi; od;
  if b=a+1 then a:=b; print(n); j:=1;
     while v[b+j]>0 do a:=b+j; print(v[b+j]); j:=j+1; od;
  else if b>a+1 then if v[b]=0 then v[b]:=n; fi; fi; fi;
od; end:
A211224(1000);

PARI

ct(n)=my(t=sigma(n));sum(i=1,n\2,sigma(i)+sigma(n-i)==t)
v=vector(100);for(n=1,1e5,t=ct(n);if(t&&t<=#v&&!v[t],v[t]=n));v
\\ Charles R Greathouse IV, May 04 2012