A185351 Sums of distinct perfect numbers.

0, 6, 28, 34, 496, 502, 524, 530, 8128, 8134, 8156, 8162, 8624, 8630, 8652, 8658, 33550336, 33550342, 33550364, 33550370, 33550832, 33550838, 33550860, 33550866, 33558464, 33558470, 33558492, 33558498, 33558960, 33558966, 33558988, 33558994, 8589869056

Offset: 1

Author

Charles R Greathouse IV, Feb 09 2012

Keywords

• nonn

Comments

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

Numbers in the range of the sum of perfect divisors function (A187794). - Timothy L. Tiffin, Jul 13 2016

Examples

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A083865, A204879, A187794.

Programs

Mathematica

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

PARI

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