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.

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, 1, 84, 1, 30, 19, 20, 21, 104, 1, 22, 21, 88, 1, 102, 1, 50, 57, 26, 1, 148, 8, 54, 25, 56, 1, 98, 25, 106, 27, 32, 1, 300, 1, 34, 69, 62, 27, 134, 1, 68, 31, 144

Offset: 1

Author

Paolo Xausa, Aug 09 2023

Keywords

• nonn

Comments

Inspired by an X (or Twitter) post by Matt Henderson (see links section).

This is A364828 without the outer circle.

Links

• Matt Henderson, X post, 2023.
• Paolo Xausa, Illustration of first terms.
• Paolo Xausa, Illustration of a(60).

Crossrefs

Cf. A006600, A007678, A364828, A364830, A364838.

Formula

a(n) = 1, if n is prime.

a(n) = n - 2, if n > 1 is a power of 2.

a(n) = A364828(n) - n.