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

4, 12, 7, 22, 14, 17, 39, 0, 37, 112, -337, 1103, -2570, 5868, -12201, 24670, -47528, 88283, -155910, 259140, -393399, 512341, -456546, -191155, 2396639, -8213818, 21761218, -50922953, 110269343, -225991348, 444168748, -844390064, 1561482582, -2817844477

Offset: 1

Author

Gus Wiseman, Oct 19 2024

Keywords

• sign

Comments

These are the row-sums of the triangle-version of A377046.

Examples

			The third antidiagonal of A377046 is (9, 1, -3), so a(3) = 7.
		

Crossrefs

The version for primes is A140119, noncomposites A376683, composites A377034.

For squarefree instead of nonsquarefree numbers we have A377039.

The absolute value version is A377048.

For leading column we have A377049.

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

A000040 lists the primes, differences A001223, seconds A036263.

A005117 lists the squarefree numbers.

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

A073576 counts integer partitions into squarefree numbers, factorizations A050320.

Cf. A007674, A053797, A053806, A061398, A072284, A112925, A112926, A120992, A376311, A376591, A376592, A377051.

Programs

Mathematica

nn=20;
t=Table[Take[Differences[NestList[NestWhile[#+1&,#+1,SquareFreeQ[#]&]&,4,2*nn],k],nn],{k,0,nn}];
Total/@Table[t[[j,i-j+1]],{i,nn},{j,i}]