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Search: id:A056171
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| A056171 |
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Number of unitary prime divisors of n!. |
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+0
10
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| 0, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 3, 3, 4, 4, 4, 3, 4, 4, 4, 3, 3, 3, 4, 4, 5, 5, 5, 4, 4, 4, 5, 4, 4, 4, 5, 5, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 6, 7, 7, 8, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 9, 9, 9, 9, 9, 10, 10, 10, 9, 10, 10, 10, 9, 9, 9, 10, 10, 10, 10, 10, 9, 9, 9, 10, 10
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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A unitary prime divisor for n! is not smaller than n/2. a(n)=PrimePi[n]-PrimePi[n/2]
See the references and links mentioned in A143227. [From Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 03 2008]
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FORMULA
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A prime divisor of n is unitary iff its exponent is 1 in prime power factorization of n. In general GCD[p, n/p]=1 or p. Cases are counted when GCD[p, n/p]=1.
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EXAMPLE
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10!=2.2.2.2.2.2.2.2.3.3.3.3.5.5.7 The only unitary prime divisor is 7, so a(10)=1, while 10! has 3 non-unitary prime divisors.
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CROSSREFS
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Cf. A001221, A034444, A000720, A048105, A048656, A048657.
Cf. A014085, A060715, A104272, A143223, A143224, A143225, A143226, A143227. [From Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 03 2008]
Adjacent sequences: A056168 A056169 A056170 this_sequence A056172 A056173 A056174
Sequence in context: A082477 A036430 A128428 this_sequence A076755 A106490 A122375
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jul 27 2000
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