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

Author

Jonathan Vos Post, Jul 25 2007

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A066272, A091507, A130799.

Programs

Maple

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

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

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.

Extensions

More terms from Hakan Icoz, Dec 25 2021