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

1,1

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

Mathematica

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

Crossrefs

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

Sequence in context: A167857 A117284 A137377 * A339238 A168543 A026277

Adjacent sequences: A274790 A274791 A274792 * A274794 A274795 A274796

Keyword

nonn

Author

Timothy L. Tiffin, Jul 07 2016

Status

approved