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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

REFERENCES

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

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

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-Fran├žois Alcover, Mar 24 2014, after Alois P. Heinz *)

CROSSREFS

Sequence in context: A122601 A125776 A066977 * A161012 A065446 A159962

Adjacent sequences:  A007548 A007549 A007550 * A007552 A007553 A007554

KEYWORD

sign,look,eigen

AUTHOR

N. J. A. Sloane.

EXTENSIONS

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

STATUS

approved

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Last modified October 23 20:52 EDT 2018. Contains 316530 sequences. (Running on oeis4.)