BLM : Bureau of Land Management
The Index was extracted from the BLM site. At this time, I have only included Hourihan(e), Hourahan(e), Horihan(e), and Horahan(e). The BLM search engine accepts wild-card searches (using %) and it is easy to find variations of Horrigan, Hourigan, etc.
The index was extracted from the HeritageQuest Online site provided by ProQuest, available through your public library. Since their search engine does not support soundex nor wildcards, eight spellings were extracted: Hourihan(e), Horihan(e), Hourahan(e), and Horahan(e). The results are sorted by first name, then age, then census-state.
Note that this index was created by copying from the ProQuest index. The census pages were not examined to see if the indexing was accurate. Misspellings were copied, so you might see Michael spelled as Micheal, or Daniel as Danial.
The HeritageQuest Online site can be accessed from within many large library systems. Websites of those libraries frequently provide a link to electronic resources which allow you to access HeritageQuest Online from your home by logging in with your library card number.
Once you are logged in, type the surname as you see it in this index, then select the year and state. Follow the links to see your census image.
The Famine Years index was extracted from the NARA Access to Archival Databases
The Ellis Island links point to the search tools originated by Dr. Stephen Morse and his collaborators
ISTG is the Immigration Ships Transcribers Guild. At last look, searches found hits for "Hourihan" and "Hourahan"