A377040 - OEIS

A377040

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

1, 3, 4, 9, 13, 18, 28, 39, 106, 267, 595, 1212, 2286, 4041, 6720, 10497, 15387, 20914, 25894, 29377, 37980, 70785, 175737, 343806, 579751, 861934, 1162080, 1431880, 1688435, 2589533, 8731932, 23911101, 58109574, 130912573, 276067892, 543833014, 992784443

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..36.

EXAMPLE

The fourth antidiagonal of A377038 is (6, 1, -1, -2, -3), so a(4) = 13.

MATHEMATICA

nn=20;

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

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

CROSSREFS

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

These are the antidiagonal-sums of the absolute value of A377038.

The non-absolute version is A377039.

For nonsquarefree numbers we have A377048, non-absolute A377047.

For prime-powers we have A377053, non-absolute 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, A140119, A376311, A376590, A376591, A377046.

Sequence in context: A116552 A339996 A225288 * A167930 A326981 A124285

Adjacent sequences: A377037 A377038 A377039 * A377041 A377042 A377043

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 18 2024

STATUS

approved