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A007551
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Shifts left when Moebius transformation applied twice.
(Formerly M2313)
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1
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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
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OFFSET
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1,4
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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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]
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MAPLE
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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):
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 11 2005
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STATUS
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approved
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