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Search: id:A056812
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| A056812 |
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Number of unitary prime factors of LCM[1,...,n], i.e. primes in LCM with exponent 1. |
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+0
2
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| 0, 1, 2, 1, 2, 2, 3, 3, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 11, 11, 11, 11, 12, 12, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 19
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OFFSET
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1,3
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COMMENT
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Number of primes in the interval ]sqrt(n), n], (i.e., excluding sqrt(n) but including n). - Lekraj Beedassy (blekraj(AT)yahoo.com), Mar 31 2005
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FORMULA
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a(n)=A056169(A003418(n), also a(n)=A000720(n)-PrimePi(Sqrt{n))=A001221(A003418(n))-A000720(A000196(n))
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EXAMPLE
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n=100, LCM[100] has 25 prime factors of which only 2 and 3 has exponent larger than 1 resulting powers: 64 and 81. So 23 prime-factors are unitary, i.e. with exponent 1. So a(100)=23.
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CROSSREFS
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Cf. A056169, A003418, A000720, A001221, A000196.
Sequence in context: A085432 A029169 A129193 this_sequence A082533 A050373 A126237
Adjacent sequences: A056809 A056810 A056811 this_sequence A056813 A056814 A056815
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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), Aug 28 2000
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