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A056674
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Number of squarefree divisors which are not unitary. Also number of unitary divisors which are not squarefree.
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,12
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COMMENTS
| Numbers of unitary and of squarefree 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
| a(n)=A034444(n)-A000005[A055231(n)] a(n)=A034444(n)-A000005[A007913(n)/A055229(n)]
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EXAMPLE
| n=252, it has 18 divisors, 8 are unitary, 8 are squarefree, 2 belong to both classes, so 6 are squarefree but not unitary, thus a(252)=6. Set {2,3,14,21,42} forms squarefree but non-unitary while set {4,9,36,28,63,252} of same size gives the set of not squarefree but unitary divisors.
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CROSSREFS
| A034444, A000005, A055231, A007913, A055229 a(n)=A000005[A055231(n)]=A000005[A007913(n)/A055229(n)]
Sequence in context: A070138 A024153 A079127 * A037188 A086079 A133703
Adjacent sequences: A056671 A056672 A056673 * A056675 A056676 A056677
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Aug 10 2000
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