%I #24 Oct 19 2023 07:36:32

%S 2,3,6,2,30,15,4,42,42,10,270,54,8,33,2310,280,78,78,8,4050,4050,14,

%T 1428,102,440,6270,114,32,7938,257985,520,138,552,16,11250,866250,616,

%U 1458,1458,2720,14790,174,131040,16926,17670,190,39204,78408,8,2315250

%N Denominators of n divided by the product of the anti-divisors of n.

%C See A066272 for definition of anti-divisor.

%H Dumitru Damian, <a href="/A093396/b093396.txt">Table of n, a(n) for n = 3..10000</a>

%F a(n) = A091507(n)/GCD(n, A091507(n))

%e The anti-divisors of 18 are 4, 5, 7, 12. Hence a(18) = 4*5*7*12/GCD(4*5*7*12, 18) = 280.

%o (Python)

%o import numpy as np

%o from sympy.ntheory.factor_ import antidivisors

%o def a093396(k):

%o return (m:=np.prod(antidivisors(k), dtype=object))//np.gcd(m,k, dtype=object)

%o {print(a093396(k), end = ', ') for k in range(3,10**2)} # _Dumitru Damian_, Oct 16 2023

%Y Cf. A066417, A091507, A093394, A093395 (numerators).

%K nonn,frac

%O 3,1

%A _Lior Manor_, Mar 28 2004

%E Name changed by _Franklin T. Adams-Watters_, Aug 21 2013