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

Author

Ilya Gutkovskiy, Aug 17 2017

Keywords

• nonn

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

Crossrefs

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

Programs

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