A274793 Numbers not in the range of the sum of odd divisors function.

2, 3, 5, 7, 9, 10, 11, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 39, 41, 43, 45, 46, 47, 49, 50, 51, 52, 53, 55, 58, 59, 61, 63, 64, 65, 66, 67, 69, 70, 71, 73, 75, 76, 77, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 99, 100

Offset: 1

Author

Timothy L. Tiffin, Jul 07 2016

Keywords

• nonn

Comments

Numbers which do not appear in A000593; that is, there is no positive integer N whose sum of odd divisors is equal to a(n) for any n.

The sum of odd divisors of x is equal to sigma(x) if and only if x is odd. So, there are numbers in the range of sigma(x) that are not in the range of the sum of odd divisors function.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000593, supersequence of A007369, A274790 (complement).

Programs

Mathematica

TakeWhile[Complement[Range@ #, Union@ Table[Total@ Select[Divisors@ n, OddQ], {n, 2 #}]], Function[k, k <= #]] &@ 100 (* Michael De Vlieger, Jul 07 2016 *)