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A072453
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Shadow transform of A000522.
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6
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0, 1, 1, 0, 1, 2, 0, 0, 1, 0, 2, 0, 0, 3, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 3, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 3, 2, 0, 2, 1, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 1, 6, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 1, 0, 0, 2, 0, 0, 1, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,6
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LINKS
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Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5 (1999) 138-150. (ps, pdf); see Definition 7 for the shadow transform.
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MAPLE
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add(n!/k!, k=0..n) ;
end proc:
shadD := proc(a)
local s, n ;
s := {} ;
for n from 0 to a-1 do
s := s union {n} ;
end if;
end do:
s ;
end proc:
nops(shadD(a)) ;
# second Maple program:
b:= proc(n) option remember; n*b(n-1)+1 end: b(0):=1:
a:= n-> add(`if`(irem(b(j), n)=0, 1, 0), j=0..n-1):
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MATHEMATICA
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b[n_] := b[n] = n*b[n - 1] + 1 ; b[0] = 1;
a[n_] := Sum[If[Mod[b[j], n] == 0, 1, 0], {j, 0, n - 1}];
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CROSSREFS
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KEYWORD
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nonn,mult,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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