Construct a list of numbers

Numbers sort as strings

1^2^25^25^3^39^4^4^41^42^44^45^47^51^65^69^77^84^

84^77^69^65^51^47^45^44^42^41^4^4^39^3^25^25^2^1^

Construct another list of numbers

Numbers sorted as numbers

1^2^3^4^4^25^25^39^41^42^44^45^47^51^65^69^77^84^

84^77^69^65^51^47^45^44^42^41^39^25^25^4^4^3^2^1^