|
%I #11 Oct 07 2016 09:40:54
%S 0,0,1,2,1,4,3,6,5,4,4,10,9,12,11,10,9,16,15,18,17,16,15,22,21,20,19,
%T 18,17,28,27,30,29,28,27,26,25,36,35,34,33,40,39,42,41,40,39,46,45,44,
%U 43,42,41,52,51,50,49,48,47,58,57,60,59,58,57,56,55,66,65,64,63,70,69
%N Smallest k such that n*(n+1)*(n+2)*...*(n+k) is divisible by the product of primes up to n.
%F For any n, a(n)<n. If p is prime, a(p+1)=p-1, a(p+2)=p-2; for k>0, a(A049591(k)+3)=A049591(k)-3 etc. - _Benoit Cloitre_, Oct 24 2002
%e a(8) = 6 as 8*9*10*11*12*13 is not divisible by 2*3*5*7 but 8*9*10*11*12*13*14 is.
%t a[n_] := For[k = 0, True, k++, If[Divisible[Pochhammer[n, k+1], Times @@ Select[Range[2, n], PrimeQ]], Return[k]]]; Array[a, 73] (* _Jean-François Alcover_, Oct 07 2016 *)
%o (PARI) a(n)=if(n<0,0,k=0; while(prod(i=0,k,n+i)%prod(v=1,precprime(n),if(isprime(v),v,1))>0,k++); k)
%K nonn
%O 0,4
%A _Amarnath Murthy_, Oct 23 2002
%E More terms from _Benoit Cloitre_, Oct 24 2002
|
