The Wikipedia article on the number 62 states this, and provides a link to a (paywalled) Time article that I can't access. I found a book on Google books that chalks this up to aspects of Freud's "Jewish mysticism." However, I can't find any sources that state that the number 62 has any significance in Jewish mysticism/Jewish history or in terms of the gematria.
Was Freud actually afraid of this number?
In Freud's letters, he expressed a belief that random numbers were telling him messages about his life. When he was assigned a phone number ending in 62, he wrote to his friend Carl Jung that
it was plausible to suppose that the other figures signified the end of my life, hence 61 or 62. Suddenly method entered into my madness. The superstitious notion that I would die between the ages of 61 and 62 proves to coincide with the conviction that with The Interpretation of Dreams I had completed my life work, that there was nothing more for me to do and that I might just as well lie down and die. (letter to Jung, April 16, 1909)
However, at roughly the same time that he was given this phone number, he at random wrote the number 67 in another letter and became convinced that this, too, was somehow meaningful.
In a letter to a friend I informed him that I had finished reading the proof-sheets of The Interpretation of Dreams, and that I did not intend to make any further changes in it, “even if it contained 2,467 mistakes.” I immediately attempted to explain to myself the number... [being 43 years old, he decided the 24 represented his remaining years of life, and 67 his year of death] (Psychopathology of Everyday Life, ch. 12)
Both of these conversations take place in the context of identifying how "superstitious" reactions to apparent randomness reflected his inner fears and personality. He regarded numerology as one such superstition.
In personal analysis of this [numerological] kind, two things were especially striking. First, the absolute somnambulistic certainty with which I attacked the unknown objective point … Moreover, in these unconscious mental operations with figures, I found a tendency to superstition the origin of which had long remained unknown to me. (Psychopathology of Everyday Life, ch. 12)
Freud was not perpetually afraid of the numbers 62 or 67. He used psychoanalysis to examine himself when numbers inspired unease in him, which seems to have been the case in 1899 especially, as he feared his life's work was complete.
