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A377040 Antidiagonal-sums of absolute value of the array A377038(n,k) = n-th term of k-th differences of squarefree numbers (A005117).

%I A377040 #5 Oct 19 2024 08:31:10
%S A377040 1,3,4,9,13,18,28,39,106,267,595,1212,2286,4041,6720,10497,15387,
%T A377040 20914,25894,29377,37980,70785,175737,343806,579751,861934,1162080,
%U A377040 1431880,1688435,2589533,8731932,23911101,58109574,130912573,276067892,543833014,992784443
%N A377040 Antidiagonal-sums of absolute value of the array A377038(n,k) = n-th term of k-th differences of squarefree numbers (A005117).
%e A377040 The fourth antidiagonal of A377038 is (6, 1, -1, -2, -3), so a(4) = 13.
%t A377040 nn=20;
%t A377040 t=Table[Take[Differences[NestList[NestWhile[#+1&,#+1,!SquareFreeQ[#]&]&,1,2*nn],k],nn],{k,0,nn}];
%t A377040 Total/@Table[Abs[t[[j,i-j+1]]],{i,nn},{j,i}]
%Y A377040 The version for primes is A376681, noncomposites A376684, composites A377035.
%Y A377040 These are the antidiagonal-sums of the absolute value of A377038.
%Y A377040 The non-absolute version is A377039.
%Y A377040 For nonsquarefree numbers we have A377048, non-absolute A377047.
%Y A377040 For prime-powers we have A377053, non-absolute A377052.
%Y A377040 A000040 lists the primes, differences A001223, seconds A036263.
%Y A377040 A005117 lists the squarefree numbers, complement A013929 (differences A078147).
%Y A377040 A073576 counts integer partitions into squarefree numbers, factorizations A050320.
%Y A377040 A377041 gives first column of A377038, for primes A007442 or A030016.
%Y A377040 A377042 gives first position of 0 in each row of A377038.
%Y A377040 Cf. A007674, A053797, A053806, A061398, A072284, A075526, A076259, A120992, A140119, A376311, A376590, A376591, A377046.
%K A377040 nonn
%O A377040 0,2
%A A377040 _Gus Wiseman_, Oct 18 2024