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A055081
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Number of positive integers whose harmonic mean with n is a positive integer.
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3
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1, 2, 3, 3, 3, 7, 3, 4, 5, 6, 3, 10, 3, 6, 10, 5, 3, 11, 3, 10, 9, 6, 3, 13, 5, 6, 7, 10, 3, 20, 3, 6, 9, 6, 10, 16, 3, 6, 9, 13, 3, 20, 3, 9, 17, 6, 3, 16, 5, 10, 9, 9, 3, 15, 9, 13, 9, 6, 3, 30, 3, 6, 16, 7, 9, 20, 3, 9, 9, 19, 3, 22, 3, 6, 16, 9, 10, 19, 3, 16, 9, 6, 3, 30, 9, 6, 9, 13, 3, 33
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also the number of factors of 2n^2 which are less than 2n, since the harmonic mean of n and 2n^2/k-n is 2n-k and these are all positive integers iff k<2n is a factor of 2n^2. So a(n)=3 iff n=4 or n is an odd prime.
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EXAMPLE
| a(6)=7 since the pairwise harmonic means of 6 with 2, 3, 6, 12, 18, 30 and 66 are 3, 4, 6, 8, 9, 10 and 11 respectively.
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CROSSREFS
| The smallest and largest positive integers whose harmonic means with n are positive integers are A053626 and A000384 with harmonic means of A053627 and A004273.
Sequence in context: A168113 A170895 A141479 * A109833 A132005 A088041
Adjacent sequences: A055078 A055079 A055080 * A055082 A055083 A055084
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KEYWORD
| nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jun 13 2000
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