A291109 Numbers that are not the sum of the squarefree divisors of some natural number.

2, 5, 7, 9, 10, 11, 13, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 37, 39, 40, 41, 43, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 63, 64, 65, 66, 67, 69, 70, 71, 73, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 99, 100, 101, 103, 105, 106, 107, 109, 111

Offset

1,1

Comments

Impossible values for A048250 (numbers k in increasing order such that A048250(m) = k has no solution).

Numbers that are not of the form Product (p_i + 1), p is a prime, so all odd numbers (except 1 and 3) are in this sequence.

Also numbers that are not the sum of the divisors of some squarefree number.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sums of divisors

Maple

sort(convert({$1..1000} minus map(numtheory:-sigma, select(numtheory:-issqrfree, {$1..1000})), list)); # Robert Israel, Jun 26 2018

Mathematica

TakeWhile[Complement[Range@ #, Union@ Table[Total@ Select[Divisors@ n, SquareFreeQ], {n, 2 #}]], Function[k, k <= #]] &@ 111

Crossrefs

Cf. A005114, A005117, A007369, A048250, A048995, A062822, A063948, A064000, A203444, A206778, A274793.

Sequence in context: A104428 A349830 A241884 * A365169 A050114 A325171

Adjacent sequences: A291106 A291107 A291108 * A291110 A291111 A291112

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 17 2017

Status

approved