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

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..2309

Index entries for sequences related to primorial numbers

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)

Example

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

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 *)

Prog

(Scheme) (define (A053589 n) (A002110 (A276084 n))) ;; Antti Karttunen, 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

Crossrefs

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

Sequence in context: A126083 A356158 A071416 * A055770 A225821 A368777

Adjacent sequences: A053586 A053587 A053588 * A053590 A053591 A053592

Keyword

nonn,easy

Author

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

Extensions

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

Status

approved