A377469 a(n) = (A003309(n)-1)*a(n-1) (n > 1), a(1) = 1, where A003309 are the ludic numbers.

1, 1, 2, 8, 48, 480, 5760, 92160, 2027520, 48660480, 1362493440, 49049763840, 1961990553600, 82403603251200, 3790565749555200, 197109418976870400, 11826565138612224000, 780553299148406784000, 54638730940388474880000, 4152543551469524090880000, 340508571220500975452160000

Offset: 1

Author

M. F. Hasler, Nov 13 2024

Keywords

• nonn

Comments

The analog of A005867 for ludic numbers A003309 instead of primes A000040. Since A003309(9) = 23 > A000040(8) = 19 is the first term that differs in the two sequences (up to offset and initial 1's), this sequence differs from A005867 also from the 9th term on, which is a(9) = (23-1)*92160 = 2027520 instead of A005867(8) = (19-1)*92160 = 1658880.

This sequence gives the (pseudo) period lengths of the rows of the ludic sieve array A255127, in which row r is pseudo-periodic, A255127(r, c) = A255127(r, c-a(r)) + S(r), with the shift S(r) given by the ludic factorials A376237.

Examples

			Since A003309 = (1, 2, 3, 5, 7, 11, 13,17, 23, 25, ...), we get:
a(2) = (2-1)*1 = 1, a(3) = (3-1)*1 = 2, a(4) = (5-1)*2 = 8, a(5) = (7-1)*8 = 48,
a(6) = (11-1)*48 = 480, a(7) = (13-1)*480 = 5760, a(8) = (17-1)*2 = 92160,
a(9) = (23-1)*92160 = 2027520, a(10) = (25-1)*2027520 = 48660480, and so on.
		

Crossrefs

Cf. A003309 (ludic numbers), A255127 (ludic sieve array), A376237 (ludic factorials), A005867 (analog of this sequence for primes), A000040 (the primes).

Programs

PARI

apply( {A377469(n) = if(n>1, (A003309(n)-1)*A377469(n-1), 1)}, [1..19])

Formula

a(n) = A005867(n-1) up to n = 8.