A377047 - OEIS

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

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OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..34.

EXAMPLE

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

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}]

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.

Sequence in context: A133517 A258565 A335914 * A331054 A372651 A361192

Adjacent sequences: A377044 A377045 A377046 * A377048 A377049 A377050

KEYWORD

sign

AUTHOR

Gus Wiseman, Oct 19 2024

STATUS

approved