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1, 2, 1, 1, 0, 1, 3, 2, 0, 1, 1, 0, 0, 0, 1, 2, 1, 2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 4, 3, 0, 2, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 2, 3, 1, 0, 2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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The inverse Moebius transform of the first column of A115361 which is A209229 gives the first column of this sequence.
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 1..1275
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FORMULA
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T(n,k) = A001511(n/k) for k | n, T(n,k) = 0 otherwise. - Andrew Howroyd, Aug 04 2018
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EXAMPLE
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First few rows of the triangle are:
1;
2, 1;
1, 0, 1;
3, 2, 0, 1;
1, 0, 0, 0, 1;
2, 1, 2, 0, 0, 1;
1, 0, 0, 0, 0, 0, 1;
4, 3, 0, 2, 0, 0, 0, 1;
...
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MAPLE
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A129353 := proc(n, k)
add( A051731(n, j)*A115361(j-1, k-1), j=k..n) ;
end proc: # R. J. Mathar, Jul 14 2012
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MATHEMATICA
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T[n_, k_] := If[Mod[n, k] != 0, 0, 1 + IntegerExponent[n/k, 2]];
Table[T[n, k], {n, 1, 15}, {k, 1, n}] // Flatten (* Jean-François Alcover, Apr 08 2020, from PARI *)
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PROG
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(PARI) T(n, k)={if(n%k, 0, 1 + valuation(n/k, 2))} \\ Andrew Howroyd, Aug 04 2018
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CROSSREFS
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Column 1 is A001511.
Row sums are A129628 (inverse Moebius transform of A001511).
Cf. A051731, A115361.
Sequence in context: A131257 A105806 A129501 * A174295 A158511 A092921
Adjacent sequences: A129350 A129351 A129352 * A129354 A129355 A129356
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson, Apr 10 2007
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STATUS
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approved
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