A377048 Antidiagonal-sums of the absolute value of the array A377046(n,k) = n-th term of k-th differences of nonsquarefree numbers (A013929).

4, 12, 13, 22, 28, 31, 39, 64, 85, 132, 395, 1103, 2650, 5868, 12297, 24694, 47740, 88731, 157744, 265744, 418463, 605929, 805692, 1104513, 2396645, 8213998, 21761334, 50923517, 110270883, 225997492, 444193562, 844498084, 1561942458, 2819780451, 4973173841

Offset: 1

Author

Gus Wiseman, Oct 19 2024

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

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

For squarefree instead of nonsquarefree numbers we have A377040.

The non-absolute version is A377047.

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, A376591, A376592.

Programs

Mathematica

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