cp's OEIS Frontend

A377035 Antidiagonal-sums of the absolute value of the array A377033(n,k) = n-th term of the k-th differences of the composite numbers (A002808).

%I A377035 #6 Oct 19 2024 08:32:26
%S A377035 4,8,10,12,14,18,21,28,34,40,47,74,96,110,138,286,715,2393,8200,25731,
%T A377035 72468,184716,431575,934511,1892267,3605315,6494464,11116110,18134549,
%U A377035 28348908,42701927,62290660,88313069,120999433,159769475,221775851,483797879
%N A377035 Antidiagonal-sums of the absolute value of the array A377033(n,k) = n-th term of the k-th differences of the composite numbers (A002808).
%e A377035 The fourth antidiagonal of A377033 is (9, 1, -1, -1), so a(4) = 12.
%t A377035 q=Select[Range[120],CompositeQ];
%t A377035 t=Table[Sum[(-1)^(j-k)*Binomial[j,k]*q[[i+k]],{k,0,j}],{j,0,Length[q]/2},{i,Length[q]/2}];
%t A377035 Total/@Table[Abs[t[[j,i-j+1]]],{i,Length[q]/2},{j,i}]
%Y A377035 The version for prime instead of composite is A376681, absolute version of A140119.
%Y A377035 The version for noncomposite is A376684, absolute version of A376683.
%Y A377035 This is the antidiagonal-sums of absolute value of the array A377033.
%Y A377035 For squarefree instead of composite we have A377040, absolute version of A377039.
%Y A377035 For nonsquarefree instead of composite we have A377048, absolute version of A377047.
%Y A377035 For prime-power instead of composite we have A377053, absolute version of A377052.
%Y A377035 Other arrays of differences: A095195 (prime), A376682 (noncomposite), A377033 (composite), A377038 (squarefree), A377046 (nonsquarefree), A377051 (prime-power).
%Y A377035 A000040 lists the primes, differences A001223, seconds A036263.
%Y A377035 A002808 lists the composite numbers, differences A073783, seconds A073445.
%Y A377035 A008578 lists the noncomposites, differences A075526.
%Y A377035 Cf. A018252, A065310, A065890, A333254, A376602 (zero), A376603 (nonzero), A376651 (positive), A376652 (negative), A376680, A377036.
%K A377035 nonn
%O A377035 1,1
%A A377035 _Gus Wiseman_, Oct 18 2024