A080497 a(n) = (n-p_1)(n-p_2)...(n-p_k) where p_k is the k-th prime and is also the largest prime < n.

1, 1, 1, 2, 6, 12, 40, 90, 336, 840, 1728, 3150, 10560, 24948, 99840, 270270, 604800, 1201200, 4386816, 11277630, 49029120, 143896500, 348364800, 746876130, 2937876480, 8117240040, 18923520000, 39628338750, 76859228160, 140548508100, 490311843840, 1233656628750

Offset

1,4

Links

Table of n, a(n) for n=1..32.

Example

a(6) = (6-2)(6-3)(6-5) = 12. a(7) = (7-2)(7-3)(7-5) = 40.

Mathematica

a[n_] := Product[n - Prime[k], {k, 1, PrimePi[n - 1]}]; Array[a, 30] (* Amiram Eldar, Dec 01 2018 *)

Prog

(PARI) a(n) = my(mk = primepi(n-1)); prod(k=1, mk, n-prime(k)); \\ Michel Marcus, Dec 01 2018
(Python)
from math import prod
from sympy import sieve
def a(n): return prod((n-p) for p in sieve.primerange(1, n))
print([a(n) for n in range(1, 33)]) # Michael S. Branicky, Oct 13 2025

Crossrefs

Cf. A080498, A072513, A080500.

Sequence in context: A280171 A327879 A094261 * A127724 A178008 A377950

Adjacent sequences: A080494 A080495 A080496 * A080498 A080499 A080500

Keyword

nonn,easy

Author

Amarnath Murthy, Mar 19 2003

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003

More terms from Michael S. Branicky, Oct 13 2025

Status

approved