A208448 Greatest common divisors of consecutive floor-factorial numbers (A010786).

1, 1, 1, 2, 2, 6, 2, 8, 24, 60, 12, 288, 96, 84, 60, 3840, 384, 15552, 576, 14400, 20160, 221760, 576, 331776, 552960, 224640, 51840, 20321280, 2903040, 108864000, 345600, 17694720, 145981440, 51701760, 1935360, 11287019520, 1254113280, 2978519040, 10782720

Offset

1,4

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Formula

a(n) = GCD(A010786(n+1),A010786(n)).

Mathematica

GCD @@@ Partition[#, 2, 1] & [Array[Product[Quotient[#, k], {k, #}] &, 30]] (* Paolo Xausa, Feb 11 2025 *)

Prog

(Haskell)
a208448 n = a208448_list !! (n-1)
a208448_list = zipWith gcd a010786_list $ tail a010786_list
(PARI) f(n) = prod(k=1, n, n\k); \\ A010786
a(n) = gcd(f(n+1), f(n)); \\ Michel Marcus, Feb 03 2022
(Python)
from math import prod
from collections import Counter
from sympy import factorint
def A208448(n):
    def f(n):
        c, j = Counter(), 1
        while j<=n:
            k = n//j
            a = -j+(j:=n//k+1)
            c += {p:e*a for p, e in factorint(k).items()}
        return c
    x, y = f(n), f(n+1)
    return prod(p**min(x[p], y[p]) for p in x) # Chai Wah Wu, May 06 2026

Crossrefs

Cf. A010786, A208449, A208450.

Sequence in context: A305984 A193388 A291840 * A096869 A345315 A385076

Adjacent sequences: A208445 A208446 A208447 * A208449 A208450 A208451

Keyword

nonn

Author

Reinhard Zumkeller, Feb 26 2012

Status

approved