A140435 Number of new lattice points created at each step in an n X n grid that are not visible.

0, 1, 1, 3, 1, 7, 1, 7, 5, 11, 1, 15, 1, 15, 13, 15, 1, 23, 1, 23, 17, 23, 1, 31, 9, 27, 17, 31, 1, 43, 1, 31, 25, 35, 21, 47, 1, 39, 29, 47, 1, 59, 1, 47, 41, 47, 1, 63, 13, 59, 37, 55, 1, 71, 29, 63, 41, 59, 1, 87, 1, 63, 53, 63, 33, 91, 1, 71, 49, 91, 1, 95, 1, 75, 69, 79, 33, 107, 1, 95, 53

Offset

1,4

Links

Table of n, a(n) for n=1..81.

Formula

G.f.: -Sum_{k>=2} mu(k) * x^k * (1 + x^k) / (1 - x^k)^2. - Ilya Gutkovskiy, Sep 14 2021

Mathematica

g[n_] := Table[ #^2 &[m], {m, 1, n + 1}] - FoldList[Plus, 1, 2 Array[EulerPhi, n, 2]] - Most[Flatten[ Append[{0}, Table[ #^2 &[m], {m, 1, n + 1}] - FoldList[Plus, 1, 2 Array[EulerPhi, n, 2]]]]]; g[80]

Crossrefs

Cf. A018805, A100613 and A140434.

Sequence in context: A186428 A323599 A167515 * A194181 A277934 A063754

Adjacent sequences: A140432 A140433 A140434 * A140436 A140437 A140438

Keyword

nonn

Author

Gregg Whisler, Jun 25 2008

Extensions

More terms from Robert G. Wilson v, Jan 17 2011

Status

approved