A279731 Composite numbers k such that the sum of the proper divisors of k is a power of 2.

9, 10, 12, 26, 49, 56, 58, 76, 122, 332, 568, 961, 992, 1018, 2042, 3344, 4336, 8186, 16129, 16256, 32762, 37432, 82704, 227744, 266176, 269072, 299576, 856544, 2097146, 5385812, 8388602, 9834772, 16580864, 17895664, 19173944, 33554426, 34636768, 61008020, 67092481, 67100672

Offset

1,1

Comments

If m = 2^j-1 is a Mersenne prime then m^2 and m*(2^j) (twice a perfect number) are terms. If m-2 is also a prime, then 2*(m-2) is a term. - Metin Sariyar, Mar 31 2020

Links

Giovanni Resta, Table of n, a(n) for n = 1..59 (terms < 4*10^12)

Example

12 is a term because 1 + 2 + 3 + 4 + 6 = 2^4.

Mathematica

Select[Range[7*10^7], CompositeQ[#]&&IntegerQ[Log[2, Total[ Most[ Divisors[ #]]]]]&] (* Harvey P. Dale, Apr 01 2018 *)

Prog

(PARI) isok(n) = ispower(sigma(n)-n, , &k) && (k==2); \\ Michel Marcus, Dec 18 2016

Crossrefs

Cf. A001065, A046528.

Sequence in context: A078390 A354038 A216780 * A037408 A178680 A178679

Adjacent sequences: A279728 A279729 A279730 * A279732 A279733 A279734

Keyword

nonn

Author

Altug Alkan, Dec 18 2016

Status

approved