A383872 -id:A383872 - cp's OEIS frontend

A279731 Composite numbers whose sum of proper divisors 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

Altug Alkan, Dec 18 2016

nonn

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

For the first 59 terms, a(n) is either the square of a Mersenne prime or its odd part is squarefree. However, this is not always true as 44088037271892 (see A383872) is a term and its odd part is not squarefree. - Chai Wah Wu, May 19 2025

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

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

Cf. A001065, A046528.

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

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

cp's OEIS Frontend

A279731 Composite numbers whose sum of proper divisors is a power of 2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI