A364829 -id:A364829 - cp's OEIS frontend

A364828 a(n) is the number of regions inside a circle after inscribing (always starting from the same point), for each divisor d_i of n greater than 1, a regular d_i-gon.

1, 2, 4, 6, 6, 12, 8, 14, 13, 18, 12, 36, 14, 24, 28, 30, 18, 46, 20, 52, 36, 36, 24, 88, 31, 42, 40, 66, 30, 114, 32, 62, 52, 54, 56, 140, 38, 60, 60, 128, 42, 144, 44, 94, 102, 72, 48, 196, 57, 104, 76, 108, 54, 152, 80, 162, 84, 90, 60, 360, 62, 96, 132, 126

Offset: 1

Paolo Xausa, Aug 09 2023

nonn

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

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

Cf. A006600, A006533, A364829, A364830, A364838.

a(n) = n + 1, if n is prime.
a(n) = 2*(n-1), if n > 1 is a power of 2.
a(n) = A364829(n) + n.

A364830 a(n) is the number of line intersections (not coinciding with a vertex) 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.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 9, 0, 1, 4, 0, 0, 8, 0, 11, 4, 1, 0, 29, 0, 1, 0, 11, 0, 43, 0, 0, 4, 1, 8, 50, 0, 1, 4, 39, 0, 49, 0, 11, 24, 1, 0, 73, 0, 12, 4, 11, 0, 33, 8, 43, 4, 1, 0, 193, 0, 1, 28, 0, 8, 57, 0, 11, 4, 71, 0, 164, 0, 1, 28, 11, 12, 61

Offset: 1

Paolo Xausa, Aug 09 2023

nonn

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

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

Cf. A006561, A007569, A032741, A364828, A364829, A364838.

a(n) = 0 if n is prime, a power of 2 or A032741(n) <= 2.

a(n) = A364838(n) - n.

A364838 a(n) is the number of line intersections (including vertices) 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.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 7, 8, 9, 11, 11, 21, 13, 15, 19, 16, 17, 26, 19, 31, 25, 23, 23, 53, 25, 27, 27, 39, 29, 73, 31, 32, 37, 35, 43, 86, 37, 39, 43, 79, 41, 91, 43, 55, 69, 47, 47, 121, 49, 62, 55, 63, 53, 87, 63, 99, 61, 59, 59, 253, 61, 63, 91, 64, 73, 123, 67

Offset: 1

Paolo Xausa, Aug 09 2023

nonn

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

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

Cf. A006561, A007569, A032741, A364828, A364829, A364830.

a(n) = n if n is prime, a power of 2 or A032741(n) <= 2.

a(n) = A364830(n) + n.

cp's OEIS Frontend

A364828 a(n) is the number of regions inside a circle after inscribing (always starting from the same point), for each divisor d_i of n greater than 1, a regular d_i-gon.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A364830 a(n) is the number of line intersections (not coinciding with a vertex) 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.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A364838 a(n) is the number of line intersections (including vertices) 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.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula