A364901 -id:A364901 - cp's OEIS frontend

A364900 The n-volume of the unit regular n-simplex is sqrt(a(n))/A364901(n), with a(n) being squarefree.

1, 1, 3, 2, 5, 3, 7, 1, 1, 5, 11, 6, 13, 7, 15, 2, 17, 1, 19, 10, 21, 11, 23, 3, 1, 13, 3, 14, 29, 15, 31, 1, 33, 17, 35, 2, 37, 19, 39, 5, 41, 21, 43, 22, 5, 23, 47, 6, 1, 1, 51, 26, 53, 3, 55, 7, 57, 29, 59, 30, 61, 31, 7, 2, 65, 33, 67, 34, 69, 35, 71, 1, 73, 37, 3

Offset: 0

Jianing Song, Aug 12 2023

a(n) = 1 if and only if n = 2*k^2 - 1 or n = 4*k^2 - 4*k for k >= 1.

a(n) = a(n+1) = 1 if and only if n = A001333(k)^2 - 2 for even k and A001333(k)^2 - 1 for odd k.

			  n |  the n-volume of the
    | unit regular n-simplex
  2 |  sqrt(3)/4 = A120011
  3 |  sqrt(2)/12 = A020829
  4 |  sqrt(5)/96 = A364895
  5 |  sqrt(3)/480
  6 |  sqrt(7)/5760
  7 |        1/20160
  8 |        1/215040
  9 |  sqrt(5)/5806080

Jianing Song, Table of n, a(n) for n = 0..10000
Wikipedia, Simplex

Cf. A007913, A364901, A120011, A020829, A364895, A001333.

a(n) = if(n%2, core((n+1)/2), core(n+1))

The n-volume of the unit regular n-simplex is sqrt(n+1)/(n!*2^(n/2)), so a(n) = A007913(n+1) for even n and A007913((n+1)/2) for odd n.

cp's OEIS Frontend

A364900 The n-volume of the unit regular n-simplex is sqrt(a(n))/A364901(n), with a(n) being squarefree.

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