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"worthless," 1845, American English, literally "of no account" (see account (n.)). The phrase of non acompte "of no value or importance" is from late 14c. Contracted form no'count is attested from 1853.
Worthless; untrustworthy; incorrigible: I'm a lazy no-account bum (1845+)noun
: A no-count that never did a right thing in his life