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A377047
Antidiagonal-sums of the array A377046(n,k) = n-th term of k-th differences of nonsquarefree numbers (A013929).
9
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
1,1
COMMENTS
These are the row-sums of the triangle-version of A377046.
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.
Sequence in context: A133517 A258565 A335914 * A331054 A372651 A361192
KEYWORD
sign,new
AUTHOR
Gus Wiseman, Oct 19 2024
STATUS
approved