This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A279731 #33 May 20 2025 00:27:45 %S A279731 9,10,12,26,49,56,58,76,122,332,568,961,992,1018,2042,3344,4336,8186, %T A279731 16129,16256,32762,37432,82704,227744,266176,269072,299576,856544, %U A279731 2097146,5385812,8388602,9834772,16580864,17895664,19173944,33554426,34636768,61008020,67092481,67100672 %N A279731 Composite numbers whose sum of proper divisors is a power of 2. %C A279731 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 %C A279731 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 %H A279731 Giovanni Resta, <a href="/A279731/b279731.txt">Table of n, a(n) for n = 1..59</a> (terms < 4*10^12) %e A279731 12 is a term because 1 + 2 + 3 + 4 + 6 = 2^4. %t A279731 Select[Range[7*10^7],CompositeQ[#]&&IntegerQ[Log[2,Total[ Most[ Divisors[ #]]]]]&] (* _Harvey P. Dale_, Apr 01 2018 *) %o A279731 (PARI) isok(n) = ispower(sigma(n)-n,,&k) && (k==2); \\ _Michel Marcus_, Dec 18 2016 %Y A279731 Cf. A001065, A046528. %K A279731 nonn %O A279731 1,1 %A A279731 _Altug Alkan_, Dec 18 2016