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Revision History for A019536
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Number of length n necklaces with integer entries that cover an initial interval of positive integers.
(history; published version)
(history; published version)
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FORMULA
From Richard L. Ollerton, May 07 2021: (Start)
a(n) = Sum_{k=1..n} A000670(gcd(n,k)).
a(n) = Sum_{k=1..n} A000670(n/gcd(n,k))*phi(gcd(n,k))/phi(n/gcd(n,k)). (End)
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editing
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approved
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reviewed
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proposed
FORMULA
The first formula is due to __Philippe Deléham_ from the Crossrefs (see also the programs below). The second one follows easily from the first one. The third one follows from the second one using the associative property of Dirichlet convolutions.
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