A076981 Smallest k such that n*(n+1)*(n+2)*...*(n+k) is divisible by the product of primes up to n.

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, 18, 17, 28, 27, 30, 29, 28, 27, 26, 25, 36, 35, 34, 33, 40, 39, 42, 41, 40, 39, 46, 45, 44, 43, 42, 41, 52, 51, 50, 49, 48, 47, 58, 57, 60, 59, 58, 57, 56, 55, 66, 65, 64, 63, 70, 69

Offset

1,4

Links

Table of n, a(n) for n=1..73.

Formula

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

Example

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.

Mathematica

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 *)

Prog

(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)

Crossrefs

Sequence in context: A361189 A004560 A345668 * A355678 A355679 A147965

Adjacent sequences: A076978 A076979 A076980 * A076982 A076983 A076984

Keyword

nonn

Author

Amarnath Murthy, Oct 23 2002

Extensions

More terms from Benoit Cloitre, Oct 24 2002

Offset corrected by Sean A. Irvine, Apr 24 2025

Status

approved