OFFSET
1,1
COMMENTS
Subset of A211223.
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..100
EXAMPLE
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.
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);
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, May 04 2012
STATUS
approved