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

1,2

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A073485 (fixed points), A192280.

Sequence in context: A363484 A056552 A049273 * A208644 A162323 A165743

Adjacent sequences: A053587 A053588 A053589 * A053591 A053592 A053593

Keyword

nice,nonn,easy

Author

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

Extensions

Data corrected by Reinhard Zumkeller, May 28 2012

Status

approved