A051466 - OEIS

%I #25 Dec 27 2019 18:25:27

%S 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 144,180,192,210,216,240,256,288,360,384,420,432,180,480,512,360,576,

%U 420,432,720,768,840,864,900,960,1024,1080,1152,210,1260,1296,1440

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

%C Note that A036041(A025487(n)) = A036041(a(n)) + 1 since A025487(n)/a(n) is prime.

%H Reinhard Zumkeller, <a href="/A051466/b051466.txt">Table of n, a(n) for n = 2..10000</a>

%F a(n) = A025487(n) / p, where p is the largest prime such that p^A051282(n) | A025487(n). - _Charlie Neder_, Oct 12 2018

%e 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 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 (* First, load second program at A025487, then: *)

%t 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 (Haskell)

%o a051466 n = a051466_list !! (n-2)

%o a051466_list = f [head a025487_list] $ tail a025487_list where

%o    f us (v:vs) = fromJust (find (\x -> mod v x == 0) us) : f (v : us) vs

%o -- _Reinhard Zumkeller_, Jul 17 2013

%Y Cf. A036041, A034776.

%K easy,nice,nonn

%O 2,2

%A _Alford Arnold_

%E Offset updated by _Matthew Vandermast_, Jul 03 2012

%E Name edited by _Charlie Neder_, Oct 20 2018

%E Name clarified by _Antti Karttunen_, Dec 24 2019