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#26 by Alois P. Heinz at Wed Jul 24 21:09:30 EDT 2024
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#25 by Amiram Eldar at Wed Jul 24 03:24:12 EDT 2024
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#24 by Amiram Eldar at Wed Jul 24 02:45:55 EDT 2024
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| KEYWORD
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nonn,easy,changed
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#23 by Amiram Eldar at Wed Jul 24 02:44:42 EDT 2024
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| FORMULA
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A prime divisor of x is non-unitary iff its exponent is at least 2 in the prime power factorization of x. In general, GCD[(p, x/p]=) = 1 or p. Cases are counted when GCD[(p, n/p]>) > 1.
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| EXAMPLE
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10!=2*2*2*2*2*2*2*! = 2*3*3*3*^8 * 3*5*^4 * 5*^2 * 7. The non-unitary prime divisors are 2, 3, and 5 because their exponents exceed 1, so a(10)=) = 3. The only unitary prime divisor of 10! is 7.
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#22 by Amiram Eldar at Wed Jul 24 02:43:05 EDT 2024
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#21 by Amiram Eldar at Wed Jul 24 02:42:18 EDT 2024
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#20 by Wesley Ivan Hurt at Sun Dec 24 09:54:40 EST 2023
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#19 by Wesley Ivan Hurt at Sun Dec 24 09:54:18 EST 2023
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| COMMENTS
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A non-unitary prime divisor for n! cannot exceed n/2. a(n) =PrimePi(n/2)..
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| FORMULA
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a(n) = pi(n/2).
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| STATUS
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approved
editing
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#18 by Bruno Berselli at Wed Apr 26 02:48:02 EDT 2017
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#17 by G. C. Greubel at Tue Apr 25 22:44:48 EDT 2017
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