

A291109


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


1



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
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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



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.


KEYWORD

nonn


AUTHOR



STATUS

approved



