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A051466 Largest product of primorials less than A025487(n) that divides A025487(n).

%I A051466 #25 Dec 27 2019 18:25:27
%S A051466 1,2,2,4,6,8,12,6,16,12,24,30,32,36,48,60,64,72,60,96,30,72,120,128,
%T A051466 144,180,192,210,216,240,256,288,360,384,420,432,180,480,512,360,576,
%U A051466 420,432,720,768,840,864,900,960,1024,1080,1152,210,1260,1296,1440
%N A051466 Largest product of primorials less than A025487(n) that divides A025487(n).
%C A051466 Note that A036041(A025487(n)) = A036041(a(n)) + 1 since A025487(n)/a(n) is prime.
%H A051466 Reinhard Zumkeller, <a href="/A051466/b051466.txt">Table of n, a(n) for n = 2..10000</a>
%F A051466 a(n) = A025487(n) / p, where p is the largest prime such that p^A051282(n) | A025487(n). - _Charlie Neder_, Oct 12 2018
%e A051466 A025487 = 1, 2, 4, 6, 8, 12, 16, 24, 30, 32, 36, ...; a(n)= 1, 2, 2, 4, 6, 8, 12, 6, 16, 12, ... . (12 divides 36, but 16 through 32 do not.)
%e A051466 A025487(38) = 900 = 5#*5#. The largest product of primorials that divides this number will be 5#*3# = 180 = a(38). - _Charlie Neder_, Oct 20 2018
%t A051466 (* First, load second program at A025487, then: *)
%t A051466 With[{s = Union@ Flatten@ f[5]}, Table[SelectFirst[Reverse@ Take[s, n - 1], Mod[s[[n]], #] == 0 &], {n, 2, Length@ s}]] (* _Michael De Vlieger_, Dec 27 2019 *)
%o A051466 (Haskell)
%o A051466 a051466 n = a051466_list !! (n-2)
%o A051466 a051466_list = f [head a025487_list] $ tail a025487_list where
%o A051466    f us (v:vs) = fromJust (find (\x -> mod v x == 0) us) : f (v : us) vs
%o A051466 -- _Reinhard Zumkeller_, Jul 17 2013
%Y A051466 Cf. A036041, A034776.
%K A051466 easy,nice,nonn
%O A051466 2,2
%A A051466 _Alford Arnold_
%E A051466 Offset updated by _Matthew Vandermast_, Jul 03 2012
%E A051466 Name edited by _Charlie Neder_, Oct 20 2018
%E A051466 Name clarified by _Antti Karttunen_, Dec 24 2019