cp's OEIS Frontend

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

%I A211224 #14 May 24 2012 20:59:10
%S A211224 3,32,117,183,393,728,933,2193,2528,1173,6136,2990,4070,8211,11488,
%T A211224 12616,6112,22287,20584,37468,38675,35245,41416,55825,43616,66385,
%U A211224 56810,94040,88736,93975,90068,174515,169376,146965,139196,210453,140576,177248
%N A211224 Least k with precisely n partitions k = x + y satisfying sigma(k) = sigma(x) + sigma(y).
%C A211224 Subset of A211223.
%H A211224 Donovan Johnson, <a href="/A211224/b211224.txt">Table of n, a(n) for n = 1..100</a>
%e A211224 a(7)=933; 933 has 7 partitions of two numbers, x and y, for which sigma(933) = sigma(x) + sigma(y) = 1248. In fact:
%e A211224 sigma(311) + sigma(622) = 312 + 936 = 1248;
%e A211224 sigma(322) + sigma(611) = 576 + 672 = 1248;
%e A211224 sigma(370) + sigma(563) = 684 + 564 = 1248;
%e A211224 sigma(391) + sigma(542) = 432 + 816 = 1248;
%e A211224 sigma(398) + sigma(535) = 600 + 648 = 1248;
%e A211224 sigma(407) + sigma(526) = 456 + 792 = 1248;
%e A211224 sigma(442) + sigma(491) = 756 + 492 = 1248;
%e A211224 Furthermore 933 is the minimum number to have this property.
%p A211224 with(numtheory);
%p A211224 A211224:=proc(q)
%p A211224 local a,b,i,j,n,v;
%p A211224 v:=array(1..10000); for n from 1 to 10000 do v[n]:=0; od;
%p A211224 a:=0;
%p A211224 for n from 1 to q do
%p A211224   b:=0;
%p A211224   for i from 1 to trunc(n/2) do
%p A211224     if sigma(i)+sigma(n-i)=sigma(n) then b:=b+1; fi; od;
%p A211224   if b=a+1 then a:=b; print(n); j:=1;
%p A211224      while v[b+j]>0 do a:=b+j; print(v[b+j]); j:=j+1; od;
%p A211224   else if b>a+1 then if v[b]=0 then v[b]:=n; fi; fi; fi;
%p A211224 od; end:
%p A211224 A211224(1000);
%o A211224 (PARI) ct(n)=my(t=sigma(n));sum(i=1,n\2,sigma(i)+sigma(n-i)==t)
%o A211224 v=vector(100);for(n=1,1e5,t=ct(n);if(t&&t<=#v&&!v[t],v[t]=n));v
%o A211224 \\ _Charles R Greathouse IV_, May 04 2012
%Y A211224 Cf. A083207, A204830, A204831, A211223, A211225.
%K A211224 nonn
%O A211224 1,1
%A A211224 _Paolo P. Lava_, May 04 2012