cp's OEIS Frontend

A377047 Antidiagonal-sums of the array A377046(n,k) = n-th term of k-th differences of nonsquarefree numbers (A013929).

%I A377047 #5 Oct 19 2024 21:44:07
%S A377047 4,12,7,22,14,17,39,0,37,112,-337,1103,-2570,5868,-12201,24670,-47528,
%T A377047 88283,-155910,259140,-393399,512341,-456546,-191155,2396639,-8213818,
%U A377047 21761218,-50922953,110269343,-225991348,444168748,-844390064,1561482582,-2817844477
%N A377047 Antidiagonal-sums of the array A377046(n,k) = n-th term of k-th differences of nonsquarefree numbers (A013929).
%C A377047 These are the row-sums of the triangle-version of A377046.
%e A377047 The third antidiagonal of A377046 is (9, 1, -3), so a(3) = 7.
%t A377047 nn=20;
%t A377047 t=Table[Take[Differences[NestList[NestWhile[#+1&,#+1,SquareFreeQ[#]&]&,4,2*nn],k],nn],{k,0,nn}];
%t A377047 Total/@Table[t[[j,i-j+1]],{i,nn},{j,i}]
%Y A377047 The version for primes is A140119, noncomposites A376683, composites A377034.
%Y A377047 For squarefree instead of nonsquarefree numbers we have A377039.
%Y A377047 The absolute value version is A377048.
%Y A377047 For leading column we have A377049.
%Y A377047 For first position of 0 in each row we have A377050.
%Y A377047 A000040 lists the primes, differences A001223, seconds A036263.
%Y A377047 A005117 lists the squarefree numbers.
%Y A377047 A013929 lists the nonsquarefree numbers, differences A078147, seconds A376593.
%Y A377047 A073576 counts integer partitions into squarefree numbers, factorizations A050320.
%Y A377047 Cf. A007674, A053797, A053806, A061398, A072284, A112925, A112926, A120992, A376311, A376591, A376592, A377051.
%K A377047 sign
%O A377047 1,1
%A A377047 _Gus Wiseman_, Oct 19 2024