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A279731 Composite numbers k such that the sum of the proper divisors of k is a power of 2. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A156345 A078390 A216780 * A037408 A178680 A178679

Adjacent sequences:  A279728 A279729 A279730 * A279732 A279733 A279734

KEYWORD

nonn

AUTHOR

Altug Alkan, Dec 18 2016

STATUS

approved

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Last modified July 29 05:30 EDT 2021. Contains 346340 sequences. (Running on oeis4.)