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

1,2

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

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A083865, A204879, A187794.

Sequence in context: A338125 A259917 A083865 * A272971 A117948 A252234

Adjacent sequences: A185348 A185349 A185350 * A185352 A185353 A185354

Keyword

nonn

Author

Charles R Greathouse IV, Feb 09 2012

Status

approved