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A140434 Number of new visible points created at each step in an n X n grid. 8
1, 2, 4, 4, 8, 4, 12, 8, 12, 8, 20, 8, 24, 12, 16, 16, 32, 12, 36, 16, 24, 20, 44, 16, 40, 24, 36, 24, 56, 16, 60, 32, 40, 32, 48, 24, 72, 36, 48, 32, 80, 24, 84, 40, 48, 44, 92, 32, 84, 40, 64, 48, 104, 36, 80, 48, 72, 56, 116, 32, 120 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Equals row sums of triangle A143467. - Gary W. Adamson, Aug 17 2008

Equals first difference row of A018805: (1, 3, 7, 11, 19, 23, 35,...). - Gary W. Adamson, Aug 17 2008

a(n) is the number of rationals p/q such that |p| + |q| = n. - Geoffrey Critzer, Oct 11 2011

a(n) is the number of nonempty lists of positive integers whose continuants are equal to n. For example, for n = 6 these continuants are [6], [5,1], [1,5], and [1,4,1]. - Jeffrey Shallit, May 18 2016

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = 2 phi(n), where phi is Euler's phi function, A000010, for n >= 2.

Sum_{k=1..n} a(k)*floor(n/k) = n^2. - Benoit Cloitre, Nov 09 2016

EXAMPLE

G.f. = x + 2*x^2 + 4*x^3 + 4*x^4 + 8*x^5 + 4*x^6 + 12*x^7 + 8*x^8 + 12*x^9 + ...

MATHEMATICA

f[n_] := FoldList[Plus, 1, 2 Array[EulerPhi, n, 2]] // Differences // Prepend[#, 1]&

a[ n_] := If[ n < 3, Max[0, n], Sum[ MoebiusMu[d] (2 n/d - 1 - Mod[n/d, 2]), {d, Divisors@n}]]; (* Michael Somos, Jul 24 2015 *)

PROG

(Haskell)

a140434 n = a140434_list !! (n-1)

a140434_list = 1 : zipWith (-) (tail a018805_list) a018805_list

-- Reinhard Zumkeller, May 04 2014

(PARI) {a(n) = if( n<3, max(0, n), sumdiv(n, d, moebius(d) * (2*n/d - 1 - (n/d)%2)))}; /* Michael Somos, Jul 24 2015 */

CROSSREFS

Cf. A018805, A100613, A140435. Equals twice A000010 (for n >= 2).

Sequence in context: A162943 A131136 A117973 * A308605 A107748 A005884

Adjacent sequences:  A140431 A140432 A140433 * A140435 A140436 A140437

KEYWORD

nonn

AUTHOR

Gregg Whisler, Jun 25 2008, Jun 28 2008

EXTENSIONS

Mathematica simplified by Jean-Fran├žois Alcover, Jun 06 2013

STATUS

approved

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Last modified April 6 15:41 EDT 2020. Contains 333276 sequences. (Running on oeis4.)