A377048 - OEIS

%I #5 Oct 19 2024 21:44:20

%S 4,12,13,22,28,31,39,64,85,132,395,1103,2650,5868,12297,24694,47740,

%T 88731,157744,265744,418463,605929,805692,1104513,2396645,8213998,

%U 21761334,50923517,110270883,225997492,444193562,844498084,1561942458,2819780451,4973173841

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

%C These are the row-sums of the absolute value triangle version of A377046.

%e The third antidiagonal of A377046 is (9, 1, -3), so a(3) = 13.

%t nn=20;

%t t=Table[Take[Differences[NestList[NestWhile[#+1&, #+1,SquareFreeQ[#]&]&,4,2*nn],k],nn],{k,0,nn}];

%t Total/@Table[Abs[t[[j,i-j+1]]],{i,nn},{j,i}]

%Y The version for primes is A376681, noncomposites A376684, composites A377035.

%Y For squarefree instead of nonsquarefree numbers we have A377040.

%Y The non-absolute version is A377047.

%Y For leading column we have A377049.

%Y For first position of 0 in each row we have A377050.

%Y A000040 lists the primes, differences A001223, seconds A036263.

%Y A005117 lists the squarefree numbers.

%Y A013929 lists the nonsquarefree numbers, differences A078147, seconds A376593.

%Y A073576 counts integer partitions into squarefree numbers, factorizations A050320.

%Y Cf. A007674, A053797, A053806, A061398, A072284, A112925, A112926, A120992, A376591, A376592.

%K nonn

%O 1,1

%A _Gus Wiseman_, Oct 19 2024