

A076981


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


0



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
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OFFSET

0,4


LINKS

Table of n, a(n) for n=0..72.


FORMULA

For any n, a(n)<n. If p is prime, a(p+1)=p1, a(p+2)=p2; 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] (* JeanFrançois 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: A234586 A186421 A004560 * A147965 A167542 A167419
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


STATUS

approved



