A053589 Greatest primorial number (A002110) which divides n.

1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 30, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 30, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 30, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6

Offset: 1

Author

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

Keywords

• nonn
• easy

Examples

			a(30) = 30 because 30=2*3*5, a(15) = 1 because 15=3*5.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..2309
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A002110, A276084, A053669, A111701, A276151, A276152, A276157, A260188, A276086, A276150.

Programs

Maple

N:= 1000: # to get a(1)..a(N)
P:= 1: p:= 1:
A:= Vector(N,1):
do
  p:= nextprime(p);
  P:= P*p;
  if P > N then break fi;
  A[[seq(i,i=P..N,P)]]:= P;
od:
convert(A,list); # Robert Israel, Aug 30 2016

Mathematica

Table[k = 1; While[Divisible[n, Times @@ Prime@ Range@ k], k++]; Times @@ Prime@ Range[k - 1], {n, 120}] (* Michael De Vlieger, Aug 30 2016 *)

PARI

a(n)=my(f=factor(n), r = 1, k = 1, p); while(k<=matsize(f)[1], p=prime(k); if(f[k,1]!=p,return(r));r*=p; k++) ; r
a(n) = my(r = 1, p = 2); while(n/p==n\p, r*=p; p=nextprime(p+1));r
\\ list of all terms up to n#.
lista(n) = my(l = List([1]),k,s=1); forprime(i=2,n, for(j=1,i-1, for(k=1,s, listput(l,l[k]))); l[#l]*=i; s=#l); l \\ David A. Corneth, Aug 30 2016

PARI

a(n)=my(s=1); forprime(p=2,, if(n%p, return(s), s *= p)) \\ Charles R Greathouse IV, Sep 07 2016

Scheme

(define (A053589 n) (A002110 (A276084 n))) ;; Antti Karttunen, Aug 30 2016

Formula

From Antti Karttunen, Aug 30 2016: (Start)

a(n) = A002110(A276084(n)).

a(n) = n/A111701(n).

A276157(n) = A260188(n)/a(n).

(End)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Oct 02 2000