A130874 Anti-divisorial numbers: the product of all anti-divisors of all integers less than or equal to n.

2, 6, 36, 144, 4320, 64800, 777600, 65318400, 2743372800, 109734912000, 29628426240000, 3199870033920000, 383984404070400000, 12671485334323200000, 29271131122286592000000, 49175500285441474560000000, 3835689022264435015680000000, 1196734974946503724892160000000

Offset

3,1

Comments

Different from the anti-primorial, which is the partial products of anti-primes.

Links

Hakan Icoz, Table of n, a(n) for n = 3..150

Formula

a(n) = Product_{k=3..n} {anti-divisors(k)} = Product_{k=3..n} Product_{j=1..A066272(k)} (j-th element of k-th row of A130799) = partial products of A091507.

Example

a(11) = (anti-divisors of 3) * (anti-divisors of 4) * ... * (anti-divisors) of 11 = (2) * (3) * (2 * 3) * (4) * (2 * 3 * 5) * (3 * 5) * (2 * 6) * (3 * 4 * 7) * (2 * 3 * 7) = 2743372800.

Maple

A130874 :=  proc(n)
    mul( A091507(i), i=1..n) ;
end proc:
seq(A130874(n), n=3..20) ; # R. J. Mathar, Jan 24 2022

Prog

(Python)
from sympy.ntheory.factor_ import antidivisors
def A130874():
    sum = 1
    i = 2 #(offset-1)
    while True:
        i += 1
        for j in antidivisors(i):
            sum *= j
        yield sum
        if i == 50:#Generator stops after calculating a(50)
            break
for i in A130874():
    print(i) # Hakan Icoz, Dec 26 2021

Crossrefs

Cf. A066272, A091507, A130799.

Sequence in context: A034526 A120824 A127564 * A019020 A236692 A323945

Adjacent sequences: A130871 A130872 A130873 * A130875 A130876 A130877

Keyword

nonn

Author

Jonathan Vos Post, Jul 25 2007

Extensions

More terms from Hakan Icoz, Dec 25 2021

Status

approved