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%I #22 Apr 25 2016 11:45:28
%S 1,2,3,2,5,6,7,2,3,2,11,6,13,2,15,2,17,6,19,2,3,2,23,6,5,2,3,2,29,30,
%T 31,2,3,2,35,6,37,2,3,2,41,6,43,2,15,2,47,6,7,2,3,2,53,6,5,2,3,2,59,
%U 30,61,2,3,2,5,6,67,2,3,2,71,6,73,2,15,2,77,6,79,2,3,2,83,6,5,2,3,2,89,30
%N Product of the longest chain of consecutive primes (starting with A020639(n)) which divides n.
%H Reinhard Zumkeller, <a href="/A053590/b053590.txt">Table of n, a(n) for n = 1..10000</a>
%e a(462)=6 because 462=2*3*7*11 and so the greatest product of the longest chain including 2 is 2*3=6.
%t a[1] = 1; a[n_] := Module[{pp}, For[pp = 1; p = FactorInteger[n][[1, 1]], Mod[n, p] == 0, p = NextPrime[p], pp *= p]; pp]; Table[a[n], {n, 1, 90}] (* _Jean-François Alcover_, Mar 04 2014 *)
%o (PARI) A053590(n) = {
%o local(a) ;
%o if (n==1,
%o return(1)
%o ) ;
%o a = A020639(n) ;
%o p = nextprime(a+1) ;
%o while(1,
%o if ( n % p ==0,
%o a *= p; p=nextprime(p+1),
%o return(a)
%o ) ;
%o ) ;
%o a ;
%o } /* R. J. Mathar, Mar 02 2012 */
%o (Haskell)
%o a053590 1 = 1
%o a053590 n = last $ takeWhile ((== 0) . (mod n)) $
%o scanl1 (*) $ dropWhile (< a020639 n) a000040_list
%o -- _Reinhard Zumkeller_, May 28 2012
%Y Cf. A073485 (fixed points), A192280.
%K nice,nonn,easy
%O 1,2
%A Frederick Magata (frederick.magata(AT)uni-muenster.de), Jan 19 2000
%E Data corrected by _Reinhard Zumkeller_, May 28 2012
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