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A007551
Shifts left when Moebius transformation applied twice.
(Formerly M2313)
1
1, 1, -1, -3, -4, -6, -2, -4, 3, 6, 16, 14, 33, 31, 37, 51, 56, 54, 55, 53, 45, 55, 25, 23, -17, -8, -72, -79, -135, -137, -235, -237, -343, -369, -479, -463, -622, -624, -732, -792, -898, -900, -1056, -1058, -1144, -1234, -1282, -1284, -1428, -1423, -1418, -1524, -1467, -1469, -1425, -1445, -1262, -1366
OFFSET
1,4
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
N. J. A. Sloane, Transforms
MAPLE
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)
# second Maple program:
with(numtheory): mobtr:= proc(p) proc(n) option remember;
add(mobius(n/d)*p(d), d=divisors(n)) end end:
a:= proc(n) option remember; `if`(n<2, 1, aa(n-1)) end:
aa:= (mobtr@@2)(a):
seq(a(n), n=1..100); # Alois P. Heinz, Jun 22 2012
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A122601 A125776 A066977 * A161012 A065446 A159962
KEYWORD
sign,look,eigen
AUTHOR
EXTENSIONS
More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 11 2005
STATUS
approved