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A056172
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Number of non-unitary prime divisors of n!.
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6
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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
| 1,6
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COMMENTS
| A non-unitary prime divisor for n! is not larger than n/2. a(n)=PrimePi[n/2]
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FORMULA
| A prime divisor of x is not unitary iff its exponent is at least 2 in 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
| 10!=2.2.2.2.2.2.2.2.3.3.3.3.5.5.7 The non-unitary prime divisors is 2,3,5 because their exponents exceed 1, so a(10)=3, while 10! has only 5 unitary prime divisor.
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CROSSREFS
| A001221, A034444, A000720, A048105, A048656, A048657.
Sequence in context: A108037 A169990 A055679 * A091373 A197637 A008621
Adjacent sequences: A056169 A056170 A056171 * A056173 A056174 A056175
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jul 27 2000
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