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A343005 a(n) is the number of dihedral symmetries D_{2m} (m >= 3) that configurations of n non-overlapping equal circles can possess. 2
0, 1, 2, 2, 3, 3, 3, 4, 4, 3, 5, 5, 3, 5, 6, 4, 5, 5, 5, 7, 5, 3, 7, 8, 4, 5, 7, 5, 7, 7, 5, 7, 5, 5, 10, 8, 3, 5, 9, 7, 7, 7, 5, 9, 7, 3, 9, 10, 6, 7, 7, 5, 7, 9, 9, 9, 5, 3, 11, 11, 3, 7, 10, 8, 9, 7, 5, 7, 9, 7, 11, 11, 3, 7, 9, 7, 9, 7, 9, 12, 6, 3, 11, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

LINKS

Table of n, a(n) for n=2..85.

FORMULA

For n >= 2, a(n) = A274010(n) - 1 = A023645(n) + A023645(n-1) = tau(n) + tau(n-1) - 3, where tau(n) = A000005(n), the number of divisors of n.

EXAMPLE

a(2) = 0 because the configuration of 2 circles only possesses D_{4} symmetry.

a(6) = 3 because configurations of 6 circles can have three dihedral symmetries: D_{12} (6 circles arranged in regular hexagon shape), D_{10} (5 circles arranged in regular pentagon shape and the other circle in the center of the pentagon), and D_{6} (6 circles arranged in equilateral triangle shape).

MATHEMATICA

Table[DivisorSigma[0, n]+DivisorSigma[0, n-1]-3, {n, 2, 85}] (* Stefano Spezia, Apr 06 2021 *)

PROG

(Python)

from sympy import divisor_count

for n in range(2, 101): print(divisor_count(n) + divisor_count(n - 1)) - 3)

CROSSREFS

Cf. A000005, A023645, A274010.

Sequence in context: A179864 A070082 A085727 * A143442 A137300 A201052

Adjacent sequences:  A343002 A343003 A343004 * A343006 A343007 A343008

KEYWORD

nonn

AUTHOR

Ya-Ping Lu, Apr 02 2021

STATUS

approved

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Last modified September 27 08:39 EDT 2021. Contains 347689 sequences. (Running on oeis4.)