The article is [Blom, G. and Fröberg, C-E., Om Myntväxling, Nordisk Matematisk Tidskrift, 1962, Vol. 10, No. 1/2 (1962), pp. 55-69] for anyone who wishes to sing along.
After reading through the article, no assumption is made on the coprimality of the $a_i$, in the sense that no added assumptions appear to be stated on the $a_i$ before the statement of the theorem.
As an aside, the Swedish used in this article is absolutely gorgeous, and is well worth the read. My only concern is that the authors assume that whoever is reading the article knows the Swedish currency system well, but not everyone is aware that there are $100$ öre in $1$ krona... to further complicate matters for modern readers, the öre (equivalent to a cent) is no longer in use in Sweden.