A053590 Product of the longest chain of consecutive primes (starting with A020639(n)) which divides n.

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, 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, 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

Offset: 1

Author

Frederick Magata (frederick.magata(AT)uni-muenster.de), Jan 19 2000

Keywords

• nice
• nonn
• easy

Examples

			a(462)=6 because 462=2*3*7*11 and so the greatest product of the longest chain including 2 is 2*3=6.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A073485 (fixed points), A192280.

Programs

Haskell

a053590 1 = 1
a053590 n = last $ takeWhile ((== 0) . (mod n)) $
                   scanl1 (*) $ dropWhile (< a020639 n) a000040_list
-- Reinhard Zumkeller, May 28 2012

Mathematica

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 *)

PARI

A053590(n) = {
    local(a) ;
    if (n==1,
        return(1)
    ) ;
    a = A020639(n) ;
    p = nextprime(a+1) ;
    while(1,
        if ( n % p ==0,
            a *= p; p=nextprime(p+1),
            return(a)
        ) ;
    ) ;
    a ;
}  /* R. J. Mathar, Mar 02 2012 */

Extensions

Data corrected by Reinhard Zumkeller, May 28 2012