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 A007551 Shifts left when Moebius transformation applied twice. (Formerly M2313) 1

%I M2313

%S 1,1,-1,-3,-4,-6,-2,-4,3,6,16,14,33,31,37,51,56,54,55,53,45,55,25,23,

%T -17,-8,-72,-79,-135,-137,-235,-237,-343,-369,-479,-463,-622,-624,

%U -732,-792,-898,-900,-1056,-1058,-1144,-1234,-1282,-1284,-1428,-1423,-1418,-1524,-1467,-1469,-1425,-1445,-1262,-1366

%N Shifts left when Moebius transformation applied twice.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Alois P. Heinz, <a href="/A007551/b007551.txt">Table of n, a(n) for n = 1..10000</a>

%H M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

%H M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%p with(numtheory): mob:=proc(m,n) if irem(m,n) = 0 then mobius(m/n) else 0: fi: end: MOBIUS:=proc(a) local b,i,d: if whattype(a) <> list then RETURN([]); fi: b:=[]: for i to nops(a) do b:=[op(b), add( mob(i,d)*a[d], d=1..i)]: od: RETURN(b); end: s:=[1]: for n from 1 to 100 do s:=[1,op(MOBIUS(MOBIUS(s)))] od: op(s);# With Transforms mob,MOBIUS (Pab Ter)

%p # second Maple program:

%p with(numtheory): mobtr:= proc(p) proc(n) option remember;

%p a:= proc(n) option remember; `if`(n<2, 1, aa(n-1)) end:

%p aa:= (mobtr@@2)(a):

%p seq(a(n), n=1..100); # _Alois P. Heinz_, Jun 22 2012

%t mobtr[p_] := Module[{f}, f[n_] := f[n] = Sum[MoebiusMu[n/d]*p[d], {d, Divisors[n]}]; f]; a[n_] := a[n] = If[n < 2, 1, aa[n-1]]; aa = mobtr @ mobtr @ a; Table[a[n], {n, 1, 60}] (* _Jean-François Alcover_, Mar 24 2014, after _Alois P. Heinz_ *)

%K sign,look,eigen

%O 1,4

%A _N. J. A. Sloane_.

%E More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 11 2005

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Last modified May 5 19:09 EDT 2021. Contains 343573 sequences. (Running on oeis4.)