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A056172
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Number of non-unitary prime divisors of n!.
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14
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0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14
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OFFSET
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1,6
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COMMENTS
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A non-unitary prime divisor for n! cannot exceed n/2.
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LINKS
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FORMULA
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a(n) = pi(n/2).
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! = 2^8 * 3^4 * 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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MAPLE
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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