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Search: id:A056674
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| A056674 |
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Number of square-free divisors which are not unitary. Also number of unitary divisors which are not square-free. |
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+0
1
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| 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 1, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 2, 1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 2, 2, 0, 0, 0, 2, 1, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 2, 2, 3, 0, 0, 0, 2, 0
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OFFSET
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1,12
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COMMENT
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Numbers of unitary and of square-free divisors are identical, although the 2 sets are usually different, so sizes of parts outside overlap are also equal to each other.
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FORMULA
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a(n)=A034444(n)-A000005[A055231(n)] a(n)=A034444(n)-A000005[A007913(n)/A055229(n)]
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EXAMPLE
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n=252, it has 18 divisors, 8 are unitary, 8 are square-free, 2 belong to both classes, so 6 are square-free but not unitary, thus a(252)=6. Set {2,3,14,21,42} forms square-free but non-unitary while set {4,9,36,28,63,252} of same size gives the set of not square-free but unitary divisors.
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CROSSREFS
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A034444, A000005, A055231, A007913, A055229 a(n)=A000005[A055231(n)]=A000005[A007913(n)/A055229(n)]
Sequence in context: A070138 A024153 A079127 this_sequence A037188 A086079 A133703
Adjacent sequences: A056671 A056672 A056673 this_sequence A056675 A056676 A056677
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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 10 2000
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