%I #30 Jul 14 2016 00:19:37

%S 0,6,28,34,496,502,524,530,8128,8134,8156,8162,8624,8630,8652,8658,

%T 33550336,33550342,33550364,33550370,33550832,33550838,33550860,

%U 33550866,33558464,33558470,33558492,33558498,33558960,33558966,33558988,33558994,8589869056

%N Sums of distinct perfect numbers.

%C The first 131072 terms of this sequence are even. Conjecturally, all terms are even.

%C Numbers in the range of the sum of perfect divisors function (A187794). - _Timothy L. Tiffin_, Jul 13 2016

%H Charles R Greathouse IV, <a href="/A185351/b185351.txt">Table of n, a(n) for n = 1..10000</a>

%e 502 = 496 + 6, where 496 and 6 are perfect.

%t With[{perf = Select[Range[10000], DivisorSigma[1, #] == 2# &]}, Rest[Union[Total/@Subsets[perf]]]] (* _Harvey P. Dale_, Feb 07 2012 *)

%o (PARI) vecsum(v)=sum(i=1,#v,v[i]);

%o v=apply(n->binomial(n+1,2), select(k->ispseudoprime(k), vector(15,n,2^prime(n)-1))); u=List();for(i=0,2^#v-1,listput(u,vecsum(vecextract(v,i))));vecsort(Vec(u)) \\ _Charles R Greathouse IV_, Feb 09 2012

%Y Cf. A083865, A204879, A187794.

%K nonn

%O 1,2

%A _Charles R Greathouse IV_, Feb 09 2012