The Greek adjective amerimnos (ἀμέριμνος) means free from care or anxiety — composed of the alpha-privative and merimna (anxiety, care, worry). It describes a state of freedom from the anxious preoccupation that can divide and distract the mind.
Paul uses amerimnos in 1 Corinthians 7:32 — he wants believers to be free from anxieties so they can devote themselves to God. This is the positive vision behind the Sermon on the Mount's command not to be anxious (Matthew 6:25–34). Freedom from anxiety is not achieved by suppressing worry but by redirecting trust to God through prayer and the peace of God that guards heart and mind in Christ (Philippians 4:6–7).