A216453 Number of points hidden from the central point by a closer point in a hexagonal orchard of order n.

0, 6, 12, 24, 30, 54, 60, 84, 102, 138, 144, 192, 198, 246, 288, 336, 342, 414, 420, 492, 546, 618, 624, 720, 750, 834, 888, 984, 990, 1122, 1128, 1224, 1302, 1410, 1476, 1620, 1626, 1746, 1836, 1980, 1986, 2166, 2172, 2316, 2442, 2586, 2592, 2784, 2826, 3006, 3120, 3288, 3294, 3510, 3600, 3792, 3918

Offset: 1

Author

V. Raman, Sep 07 2012

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• Project Euler, Problem 351: Hexagonal orchards.

Crossrefs

Cf. A063985.

Programs

Mathematica

Table[6*Sum[k - EulerPhi[k], {k, n}], {n, 100}] (* Jon Maiga, Jan 12 2019 *)

PARI

for(i=1,100,print1(6*(binomial(i+1,2)-sum(X=1,i,eulerphi(X))), ", "))

Formula

a(n) = 6 * (C(n+1,2) - Sum_{i=1..n} phi(i)). - corrected by Piyush Kumar and Robert Israel, Aug 26 2014

a(n) = 6*A063985(n). - Jon Maiga, Jan 12 2019