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 A242529 Number of cyclic arrangements (up to direction) of numbers 1,2,...,n such that any two neighbors are coprime. 15
 1, 1, 1, 1, 6, 2, 36, 36, 360, 288, 11016, 3888, 238464, 200448, 3176496, 4257792, 402573312, 139511808, 18240768000, 11813990400, 440506183680, 532754620416, 96429560832000, 32681097216000, 5244692024217600, 6107246661427200, 490508471914905600, 468867166554931200, 134183696369843404800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS a(n)=NPC(n;S;P) is the count of all neighbor-property cycles for a specific set S={1,2,...,n} of n elements and a specific pair-property P of "being coprime". For more details, see the link and A242519. LINKS S. Sykora, On Neighbor-Property Cycles, Stan's Library, Volume V, 2014. Wikipedia, Coprime integers FORMULA For n>2, a(n) = A086595(n)/2. EXAMPLE There are 6 such cycles of length n=5: C_1={1,2,3,4,5}, C_2={1,2,3,5,4}, C_3={1,2,5,3,4}, C_4={1,2,5,4,3}, C_5={1,3,2,5,4}, and C_6={1,4,3,2,5}. For length n=6, the count drops to just 2: C_1={1,2,3,4,5,6}, C_2={1,4,3,2,5,6}. PROG (C++) See the link. CROSSREFS Cf. A242519, A242520, A242521, A242522, A242523, A242524, A242525, A242526, A242527, A242528, A242530, A242531, A242532, A242533, A242534. Sequence in context: A096039 A201229 A038256 * A263088 A266231 A192355 Adjacent sequences:  A242526 A242527 A242528 * A242530 A242531 A242532 KEYWORD nonn,hard AUTHOR Stanislav Sykora, May 30 2014 EXTENSIONS a(1) corrected, a(19)-a(29) added by Max Alekseyev, Jul 04 2014 STATUS approved

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Last modified August 20 12:41 EDT 2018. Contains 313917 sequences. (Running on oeis4.)