The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A068781 Lesser of two consecutive numbers each divisible by a square. 30
 8, 24, 27, 44, 48, 49, 63, 75, 80, 98, 99, 116, 120, 124, 125, 135, 147, 152, 168, 171, 175, 188, 207, 224, 242, 243, 244, 260, 275, 279, 288, 296, 315, 324, 332, 342, 343, 350, 351, 360, 363, 368, 375, 387, 404, 423, 424, 440, 459, 475, 476, 495, 507, 512 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also numbers m such that mu(m)=mu(m+1)=0, where mu is the Moebius-function (A008683); A081221(a(n))>1. - Reinhard Zumkeller, Mar 10 2003 The sequence contains an infinite family of arithmetic progressions like {36a+8}={8,44,80,116,152,188,...} ={4(9a+2)}. {36a+9} provides 2nd nonsquarefree terms. Such AP's can be constructed to any term by solution of a system of linear Diophantine equation. - Labos Elemer, Nov 25 2002 1. 4k^2 + 4k is a member for all k; i.e., 8 times a triangular number is a member. 2. (4k+1) times an odd square - 1 is a member. 3. (4k+3) times odd square is a member. - Amarnath Murthy, Apr 24 2003 The asymptotic density of this sequence is 1 - 2/zeta(2) + Product_{p prime} (1 - 2/p^2) = 1 - 2 * A059956 + A065474 = 0.1067798952... (Matomäki et al., 2016). - Amiram Eldar, Feb 14 2021 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Kaisa Matomäki, Maksym Radziwiłł and Terence Tao, Sign patterns of the Liouville and Möbius functions, Forum of Mathematics, Sigma, Vol. 4. (2016), e14. FORMULA A261869(a(n)) = 0. - Reinhard Zumkeller, Sep 04 2015 EXAMPLE 44 is in the sequence because 44 = 2^2 * 11 and 45 = 3^2 * 5. MATHEMATICA Select[ Range[2, 600], Max[ Transpose[ FactorInteger[ # ]] []] > 1 && Max[ Transpose[ FactorInteger[ # + 1]] []] > 1 &] f@n_:= Flatten@Position[Partition[SquareFreeQ/@Range@2000, n, 1], Table[False, {n}]]; f@2 (* Hans Rudolf Widmer, Aug 30 2022 *) PROG (Haskell) a068781 n = a068781_list !! (n-1) a068781_list = filter ((== 0) . a261869) [1..] -- Reinhard Zumkeller, Sep 04 2015 (PARI) isok(m) = !moebius(m) && !moebius(m+1); \\ Michel Marcus, Feb 14 2021 CROSSREFS Cf. A068780, A068140, A068781, A068782, A068783, A068784, A068785. Cf. A049535, A077647, A078143, A045882. Subsequence of A261869. Sequence in context: A176297 A175496 A048109 * A212861 A333961 A038524 Adjacent sequences:  A068778 A068779 A068780 * A068782 A068783 A068784 KEYWORD nonn AUTHOR Robert G. Wilson v, Mar 04 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 6 08:17 EDT 2022. Contains 357263 sequences. (Running on oeis4.)