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A053589 Greatest primorial number (A002110) which divides n.

%I A053589 #31 Jun 04 2023 23:50:31
%S A053589 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,
%T A053589 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,
%U A053589 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
%N A053589 Greatest primorial number (A002110) which divides n.
%H A053589 Antti Karttunen, <a href="/A053589/b053589.txt">Table of n, a(n) for n = 1..2309</a>
%H A053589 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A053589 From _Antti Karttunen_, Aug 30 2016: (Start)
%F A053589 a(n) = A002110(A276084(n)).
%F A053589 a(n) = n/A111701(n).
%F A053589 A276157(n) = A260188(n)/a(n).
%F A053589 (End)
%e A053589 a(30) = 30 because 30=2*3*5, a(15) = 1 because 15=3*5.
%p A053589 N:= 1000: # to get a(1)..a(N)
%p A053589 P:= 1: p:= 1:
%p A053589 A:= Vector(N,1):
%p A053589 do
%p A053589   p:= nextprime(p);
%p A053589   P:= P*p;
%p A053589   if P > N then break fi;
%p A053589   A[[seq(i,i=P..N,P)]]:= P;
%p A053589 od:
%p A053589 convert(A,list); # _Robert Israel_, Aug 30 2016
%t A053589 Table[k = 1; While[Divisible[n, Times @@ Prime@ Range@ k], k++]; Times @@ Prime@ Range[k - 1], {n, 120}] (* _Michael De Vlieger_, Aug 30 2016 *)
%o A053589 (Scheme) (define (A053589 n) (A002110 (A276084 n))) ;; _Antti Karttunen_, Aug 30 2016
%o A053589 (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
%o A053589 a(n) = my(r = 1, p = 2); while(n/p==n\p, r*=p; p=nextprime(p+1));r
%o A053589 \\ list of all terms up to n#.
%o A053589 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
%o A053589 (PARI) a(n)=my(s=1); forprime(p=2,, if(n%p, return(s), s *= p)) \\ _Charles R Greathouse IV_, Sep 07 2016
%Y A053589 Cf. A002110, A276084, A053669, A111701, A276151, A276152, A276157, A260188, A276086, A276150.
%K A053589 nonn,easy
%O A053589 1,2
%A A053589 Frederick Magata (frederick.magata(AT)uni-muenster.de), Jan 19 2000
%E A053589 More terms from Larry Reeves (larryr(AT)acm.org), Oct 02 2000