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A129353 A051731 * A115361.

%I A129353 #18 Apr 08 2020 13:45:59
%S A129353 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,
%T A129353 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,
%U A129353 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
%N A129353 A051731 * A115361.
%C A129353 The inverse Moebius transform of the first column of A115361 which is A209229 gives the first column of this sequence.
%H A129353 Andrew Howroyd, <a href="/A129353/b129353.txt">Table of n, a(n) for n = 1..1275</a>
%F A129353 T(n,k) = A001511(n/k) for k | n, T(n,k) = 0 otherwise. - _Andrew Howroyd_, Aug 04 2018
%e A129353 First few rows of the triangle are:
%e A129353   1;
%e A129353   2, 1;
%e A129353   1, 0, 1;
%e A129353   3, 2, 0, 1;
%e A129353   1, 0, 0, 0, 1;
%e A129353   2, 1, 2, 0, 0, 1;
%e A129353   1, 0, 0, 0, 0, 0, 1;
%e A129353   4, 3, 0, 2, 0, 0, 0, 1;
%e A129353   ...
%p A129353 A129353 := proc(n,k)
%p A129353         add( A051731(n,j)*A115361(j-1,k-1),j=k..n) ;
%p A129353 end proc: # _R. J. Mathar_, Jul 14 2012
%t A129353 T[n_, k_] := If[Mod[n, k] != 0, 0, 1 + IntegerExponent[n/k, 2]];
%t A129353 Table[T[n, k], {n, 1, 15}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Apr 08 2020, from PARI *)
%o A129353 (PARI) T(n, k)={if(n%k, 0, 1 + valuation(n/k,2))} \\ _Andrew Howroyd_, Aug 04 2018
%Y A129353 Column 1 is A001511.
%Y A129353 Row sums are A129628 (inverse Moebius transform of A001511).
%Y A129353 Cf. A051731, A115361.
%K A129353 nonn,tabl
%O A129353 1,2
%A A129353 _Gary W. Adamson_, Apr 10 2007