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A377039 Antidiagonal-sums of the array A377038(n,k) = n-th term of k-th differences of squarefree numbers (A005117).

%I A377039 #6 Oct 19 2024 08:31:15
%S A377039 1,3,4,9,1,18,8,-9,106,-237,595,-1170,2276,-3969,6640,-10219,14655,
%T A377039 -18636,19666,-12071,-13056,69157,-171441,332756,-552099,798670,
%U A377039 -982472,901528,-116173,-2351795,8715186,-23856153,57926066,-130281007,273804642,-535390274
%N A377039 Antidiagonal-sums of the array A377038(n,k) = n-th term of k-th differences of squarefree numbers (A005117).
%C A377039 These are row-sums of the triangle-version of A377038.
%e A377039 The fourth antidiagonal of A377038 is (6,1,-1,-2,-3), so a(4) = 1.
%t A377039 nn=20;
%t A377039 t=Table[Take[Differences[NestList[NestWhile[#+1&,#+1,!SquareFreeQ[#]&]&,1,2*nn],k],nn],{k,0,nn}];
%t A377039 Total/@Table[t[[j,i-j+1]],{i,nn},{j,i}]
%Y A377039 The version for primes is A140119, noncomposites A376683, composites A377034.
%Y A377039 These are the antidiagonal-sums of A377038.
%Y A377039 The absolute version is A377040.
%Y A377039 For nonsquarefree numbers we have A377047.
%Y A377039 For prime-powers we have A377052.
%Y A377039 A000040 lists the primes, differences A001223, seconds A036263.
%Y A377039 A005117 lists the squarefree numbers, complement A013929 (differences A078147).
%Y A377039 A073576 counts integer partitions into squarefree numbers, factorizations A050320.
%Y A377039 A377041 gives first column of A377038, for primes A007442 or A030016.
%Y A377039 A377042 gives first position of 0 in each row of A377038.
%Y A377039 Cf. A007674, A053797, A053806, A061398, A072284, A075526, A076259, A120992, A376311, A376590, A376591, A377046.
%K A377039 sign
%O A377039 0,2
%A A377039 _Gus Wiseman_, Oct 18 2024