A117481 - OEIS

A117481

a(n) = n*(n-1)*(n-2)*(n-3)*...*(n-k) such that (n-k) is the largest prime smaller than n.

1, 2, 6, 12, 60, 30, 210, 56, 504, 5040, 55440, 132, 1716, 182, 2730, 43680, 742560, 306, 5814, 380, 7980, 175560, 4037880, 552, 13800, 358800, 9687600, 271252800, 7866331200, 870, 26970, 992, 32736, 1113024, 38955840, 1402410240, 51889178880

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = Product_{k = prevprime(n)..n} k, for n>=3 with a(1)=1, a(2)=2 and where prevprime = A151799. - Wesley Ivan Hurt, Dec 12 2021

EXAMPLE

a(10) = 10*9*8*7 = 5040 because 7 is the largest prime smaller than 10.

MATHEMATICA

a[1] = 1; a[2] = 2; a[n_] := n!/(NextPrime[n, -1] - 1)!; Array[a, 30] (* Amiram Eldar, Feb 08 2021 *)

PROG

(PARI) a(n) = if (n<=2, n, prod(k=0, n-precprime(n-1), n-k)); \\ Michel Marcus, Feb 09 2021

CROSSREFS

Cf. A151799 (prevprime v.2), A286900 (sum of the numbers from n to nextprime(n)).

Sequence in context: A231693 A375524 A232112 * A343277 A341617 A083268

Adjacent sequences: A117478 A117479 A117480 * A117482 A117483 A117484

KEYWORD

nonn,look

AUTHOR

Luc Stevens (lms022(AT)yahoo.com), Apr 25 2006

EXTENSIONS

Offset and a(36) corrected by Amiram Eldar, Feb 08 2021

STATUS

approved