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A377049
First term of the n-th differences of the nonsquarefree numbers. Inverse zero-based binomial transform of A013929.
7
4, 4, -3, 5, -6, 4, 3, -15, 25, -10, -84, 369, -1067, 2610, -5824, 12246, -24622, 47577, -88233, 155962, -259086, 393455, -512281, 456609, 191219, -2396571, 8213890, -21761143, 50923029, -110269263, 225991429, -444168664, 844390152, -1561482492, 2817844569
OFFSET
0,1
FORMULA
The inverse zero-based binomial transform of a sequence (q(0), q(1), q(2), ...) is the sequence p given by:
p(j) = sum_{k=0..j} (-1)^(j-k) binomial(j,k) q(k)
MATHEMATICA
nn=20;
Table[First[Differences[NestList[NestWhile[#+1&, #+1, SquareFreeQ[#]&]&, 4, 2*nn], k]], {k, 0, nn}]
CROSSREFS
The version for primes is A007442, noncomposites A030016, composites A377036.
For squarefree instead of nonsquarefree numbers we have A377041.
For antidiagonal-sums we have A377047, absolute A377048.
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: A073321 A055620 A072420 * A258075 A286296 A023530
KEYWORD
sign
AUTHOR
Gus Wiseman, Oct 19 2024
STATUS
approved