cp's OEIS Frontend

A377034 Antidiagonal-sums of the array A377033(n,k) = n-th term of the k-th differences of the composite numbers (A002808).

%I A377034 #6 Oct 18 2024 10:49:58
%S A377034 4,8,10,8,14,14,11,24,10,20,37,-10,56,26,-52,260,-659,2393,-8128,
%T A377034 25703,-72318,184486,-430901,933125,-1888651,3597261,-6479654,
%U A377034 11086964,-18096083,28307672,-42644743,62031050,-86466235,110902085,-110907437,52379,483682985
%N A377034 Antidiagonal-sums of the array A377033(n,k) = n-th term of the k-th differences of the composite numbers (A002808).
%C A377034 Row-sums of the triangle version of A377033.
%e A377034 The fourth antidiagonal of A377033 is (9, 1, -1, -1), so a(4) = 8.
%t A377034 q=Select[Range[100],CompositeQ];
%t A377034 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 A377034 Total/@Table[t[[j,i-j+1]],{i,Length[q]/2},{j,i}]
%Y A377034 The version for prime instead of composite is A140119, noncomposite A376683.
%Y A377034 This is the antidiagonal-sums of the array A377033, absolute version A377035.
%Y A377034 For squarefree instead of composite we have A377039, absolute version A377040.
%Y A377034 For nonsquarefree instead of composite we have A377047, absolute version A377048.
%Y A377034 For prime-power instead of composite we have A377052, absolute version A377053.
%Y A377034 Other arrays of differences: A095195 (prime), A376682 (noncomposite), A377033 (composite), A377038 (squarefree), A377046 (nonsquarefree), A377051 (prime-power).
%Y A377034 A000040 lists the primes, differences A001223, second A036263.
%Y A377034 A002808 lists the composite numbers, differences A073783, second A073445.
%Y A377034 A008578 lists the noncomposites, differences A075526.
%Y A377034 Cf. A018252, A065310, A065890, A333254, A376602 (zero), A376603 (nonzero), A376651 (positive), A376652 (negative), A376680, A377036.
%K A377034 sign
%O A377034 1,1
%A A377034 _Gus Wiseman_, Oct 17 2024