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

%I A130874 #29 Jan 24 2022 11:39:43
%S A130874 2,6,36,144,4320,64800,777600,65318400,2743372800,109734912000,
%T A130874 29628426240000,3199870033920000,383984404070400000,
%U A130874 12671485334323200000,29271131122286592000000,49175500285441474560000000,3835689022264435015680000000,1196734974946503724892160000000
%N A130874 Anti-divisorial numbers: the product of all anti-divisors of all integers less than or equal to n.
%C A130874 Different from the anti-primorial, which is the partial products of anti-primes.
%H A130874 Hakan Icoz, <a href="/A130874/b130874.txt">Table of n, a(n) for n = 3..150</a>
%F A130874 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.
%e A130874 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.
%p A130874 A130874 :=  proc(n)
%p A130874     mul( A091507(i),i=1..n) ;
%p A130874 end proc:
%p A130874 seq(A130874(n),n=3..20) ; # _R. J. Mathar_, Jan 24 2022
%o A130874 (Python)
%o A130874 from sympy.ntheory.factor_ import antidivisors
%o A130874 def A130874():
%o A130874     sum = 1
%o A130874     i = 2 #(offset-1)
%o A130874     while True:
%o A130874         i += 1
%o A130874         for j in antidivisors(i):
%o A130874             sum *= j
%o A130874         yield sum
%o A130874         if i == 50:#Generator stops after calculating a(50)
%o A130874             break
%o A130874 for i in A130874():
%o A130874     print(i) # _Hakan Icoz_, Dec 26 2021
%Y A130874 Cf. A066272, A091507, A130799.
%K A130874 nonn
%O A130874 3,1
%A A130874 _Jonathan Vos Post_, Jul 25 2007
%E A130874 More terms from _Hakan Icoz_, Dec 25 2021