A377039 Antidiagonal-sums of the array A377038(n,k) = n-th term of k-th differences of squarefree numbers (A005117).

1, 3, 4, 9, 1, 18, 8, -9, 106, -237, 595, -1170, 2276, -3969, 6640, -10219, 14655, -18636, 19666, -12071, -13056, 69157, -171441, 332756, -552099, 798670, -982472, 901528, -116173, -2351795, 8715186, -23856153, 57926066, -130281007, 273804642, -535390274

Offset

0,2

Comments

These are row-sums of the triangle-version of A377038.

Links

Table of n, a(n) for n=0..35.

Example

The fourth antidiagonal of A377038 is (6,1,-1,-2,-3), so a(4) = 1.

Mathematica

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

Crossrefs

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

These are the antidiagonal-sums of A377038.

The absolute version is A377040.

For nonsquarefree numbers we have A377047.

For prime-powers we have A377052.

A000040 lists the primes, differences A001223, seconds A036263.

A005117 lists the squarefree numbers, complement A013929 (differences A078147).

A073576 counts integer partitions into squarefree numbers, factorizations A050320.

A377041 gives first column of A377038, for primes A007442 or A030016.

A377042 gives first position of 0 in each row of A377038.

Cf. A007674, A053797, A053806, A061398, A072284, A075526, A076259, A120992, A376311, A376590, A376591, A377046.

Sequence in context: A019676 A389059 A246726 * A019900 A329212 A290373

Adjacent sequences: A377036 A377037 A377038 * A377040 A377041 A377042

Keyword

sign

Author

Gus Wiseman, Oct 18 2024

Status

approved