A077636 Length of periodic part of continued fraction expansion of square root of A051451(n), i.e., sqrt(lcm(1..x)) where x is a prime power from A000961.

0, 1, 2, 2, 4, 2, 2, 2, 4, 8, 18, 14, 36, 38, 232, 268, 110, 280, 4348, 3244, 32684, 148184, 207616, 9988, 1946132, 2154482, 13319736, 8971624, 12345748, 69705504, 159413696, 1184191340, 1183672188, 23656693528, 28963250020, 701296434876, 754283490078

Offset: 1

Author

Labos Elemer, Nov 13 2002

Keywords

• nonn
• more

Examples

			For A051451(10) = 360360, the periodic part is {3,2,1,132,1,2,3,1200} with 8 terms, so a(10) = 8.
		

Crossrefs

Cf. A000961, A003285, A051451.

Programs

Mathematica

pp = Join[{1}, Select[Range[2, 50], Mod[ #, # - EulerPhi[ # ]] == 0 &]]; Table[ Length[ Last[ ContinuedFraction[ Sqrt[ Apply[ LCM, Table[i, {i, 1, pp[[n]]}]]]]]], {n, 1, 31}]

Formula

a(n) = A003285(A051451(n)). - Michel Marcus, Sep 30 2019

Extensions

Edited and extended by Robert G. Wilson v, Nov 14 2002

a(31) from Ray Chandler, Jan 16 2009

a(32)-a(35) from Chai Wah Wu, Sep 26 2019

a(36) from Chai Wah Wu, Sep 29 2019

a(37) from Chai Wah Wu, Sep 26 2021