annoyance n.

late 13c., anoien, annuien, "to harm, hurt, injure; be troublesome or vexatious to, disquiet, upset," from Anglo-French anuier, Old French enoiier "to weary, vex, anger," anuier "be troublesome or irksome to;" according to French sources these are from Late Latin inodiare "make loathsome," from Latin (esse) in odio "(it is to me) hateful," from ablative of odium "hatred," from PIE root *od- (2) "to hate" (see odium).

Also in Middle English as a noun, "feeling of irritation, displeasure, distaste" (c. 1200, still in Shakespeare), from Old French enoi, anoi "annoyance;" the same French word was borrowed into English later in a different sense as ennui. And compare Spanish enojo "offense, injury, anger;" enojar "to molest, trouble, vex." Middle English also had annoyful and annoyous (both late 14c.).

fourteenth letter of the English alphabet; in chemistry, the symbol for nitrogen.

In late Middle English a and an commonly were joined to the following noun, if that word began with a vowel, which caused confusion over how such words ought to be divided when written separately. In nickname, newt, and British dialectal naunt, the -n- belongs to a preceding indefinite article an or possessive pronoun mine.

Other examples of this from Middle English manuscripts include a neilond ("an island," early 13c.), a narawe ("an arrow," c. 1400), a nox ("an ox," c. 1400), a noke ("an oak," early 15c.), a nappyle ("an apple," early 15c.), a negge ("an egg," 15c.), a nynche ("an inch," c. 1400), a nostryche ("an ostrich," c. 1500). My naunt for mine aunt is recorded from 13c.-17c. None other could be no noder (mid-15c.). My nown (for mine own) was frequent 15c.-18c. In 16c., an idiot sometimes became a nidiot (1530s), which, with still-common casual pronunciation, became nidget (1570s), now, alas, no longer whinnying with us.

It is "of constant recurrence" in the 15c. vocabularies, according to Thomas Wright, their modern editor. One has, among many others, Hoc alphabetum ... a nabse, from misdivision of an ABC (and pronouncing it as a word), and Hic culus ... a ners. Also compare nonce, pigsney. Even in 19c. provincial English and U.S., noration (from an oration) was "a speech; a rumor."

The process also worked in surnames, from oblique cases of Old English at "by, near," as in Nock/Nokes/Noaks from atten Oke "by the oak;" Nye from atten ye "near the lowland;" and see Nashville. (Elision of the vowel of the definite article also took place and was standard in Chancery English of the 15c.: þarchebisshop for "the archbishop," thorient for "the orient.")

But it is more common for an English word to lose an -n- to a preceding a: apron, auger, adder, umpire, humble pie, etc. By a related error in Elizabethan English, natomy or atomy was common for anatomy, noyance (annoyance) and noying (adj.) turn up 14c.-17c., and Marlowe (1590) has Natolian for Anatolian.  The tendency is not limited to English: compare Luxor, jade (n.1), lute, omelet, and Modern Greek mera for hēmera, the first syllable being confused with the article.

The mathematical use of n for "an indefinite number" is attested by 1717 in phrases such as to the nth power (see nth). In Middle English n. was written in form documents to indicate an unspecified name of a person to be supplied by the speaker or reader.