A370857 Let L_1 = (1) and L_2 = (1, 2); for any n > 2, L_n is obtained by inserting one n between each pair of consecutive terms of L_{n-1} coprime to n; a(n) gives the number of n's in L_n.

1, 1, 1, 1, 3, 1, 7, 9, 19, 13, 55, 21, 131, 157, 303, 317, 1039, 393, 2471, 2505, 5643, 6145, 19235, 7413, 40235, 51905, 110435, 110683, 359141, 45877, 764159, 1077437, 2253143, 2251065, 6699111, 2200709, 16009783, 20505321, 43172899, 29699143, 125396929

Offset: 1

Author

Rémy Sigrist, Mar 03 2024

Keywords

• nonn

Examples

			The first terms, alongside the corresponding lists, are:
  n  a(n)  L_n
  -  ----  ---------------------------------------------
  1     1  (1                                          )
  2     1  (1,                                        2)
  3     1  (1,                            3,          2)
  4     1  (1,                4,          3,          2)
  5     3  (1,          5,    4,    5,    3,    5,    2)
  6     1  (1,    6,    5,    4,    5,    3,    5,    2)
  7     7  (1, 7, 6, 7, 5, 7, 4, 7, 5, 7, 3, 7, 5, 7, 2)
		

Links

• Rémy Sigrist, PARI program

Crossrefs

Cf. A049456, A370858 (partials sums).

Programs

PARI

See Links section.

Formula

a(p) = (Sum_{k = 1, p-1} a(k)) - 1 for any odd prime number p.