A211223 - OEIS

%I #36 Jul 16 2021 03:29:04

%S 3,8,9,10,15,20,21,30,32,33,39,40,49,51,55,56,57,62,63,69,70,75,85,87,

%T 88,90,92,93,94,96,99,104,105,108,110,111,114,116,117,123,125,126,128,

%U 129,130,134,135,136,140,141,145,147,150,152,153,155,158,159,160

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

%C A211225(a(n)) > 0. - _Reinhard Zumkeller_, Jan 06 2013

%H Charles R Greathouse IV, <a href="/A211223/b211223.txt">Table of n, a(n) for n = 1..10000</a>

%e sigma(49) = sigma(8) + sigma(41) that is 57 = 15 + 42.

%e sigma(93) = sigma(31) + sigma(62) that is 128 = 32 + 96.

%e 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.

%p with(numtheory);

%p A211223:=proc(q)

%p local i,n;

%p for n from 1 to q do

%p   for i from 1 to trunc(n/2) do

%p     if sigma(i)+sigma(n-i)=sigma(n) then print(n); break; fi;

%p od; od; end:

%p A211223(10000);

%t 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 *)

%o (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

%o (Haskell)

%o a211223 n = a211223_list !! (n-1)

%o a211223_list = map (+ 1) $ findIndices (> 0) a211225_list

%o -- _Reinhard Zumkeller_, Jan 06 2013

%Y Cf. A083207, A204830, A204831, A211224, A211225.

%Y Cf. A218852.

%Y Cf. A000203.

%K nonn,nice

%O 1,1

%A _Paolo P. Lava_, Apr 27 2012