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A364829 a(n) is the number of regions inside a regular n-gon after inscribing (always starting from the same point), for each proper divisor d_i of n greater than 1, a regular d_i-gon.

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%I A364829 #14 Aug 12 2023 00:41:01
%S A364829 0,0,1,2,1,6,1,6,4,8,1,24,1,10,13,14,1,28,1,32,15,14,1,64,6,16,13,38,
%T A364829 1,84,1,30,19,20,21,104,1,22,21,88,1,102,1,50,57,26,1,148,8,54,25,56,
%U A364829 1,98,25,106,27,32,1,300,1,34,69,62,27,134,1,68,31,144
%N A364829 a(n) is the number of regions inside a regular n-gon after inscribing (always starting from the same point), for each proper divisor d_i of n greater than 1, a regular d_i-gon.
%C A364829 Inspired by an X (or Twitter) post by Matt Henderson (see links section).
%C A364829 This is A364828 without the outer circle.
%H A364829 Matt Henderson, <a href="https://twitter.com/matthen2/status/1639925895254224898">X post</a>, 2023.
%H A364829 Paolo Xausa, <a href="/A364829/a364829.pdf">Illustration of first terms</a>.
%H A364829 Paolo Xausa, <a href="/A364829/a364829_1.pdf">Illustration of a(60)</a>.
%F A364829 a(n) = 1, if n is prime.
%F A364829 a(n) = n - 2, if n > 1 is a power of 2.
%F A364829 a(n) = A364828(n) - n.
%Y A364829 Cf. A006600, A007678, A364828, A364830, A364838.
%K A364829 nonn
%O A364829 1,4
%A A364829 _Paolo Xausa_, Aug 09 2023