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A226891 Least k such that k(k+1)(k+2)(k+3) is divisible by prime(n)#. 1

%I

%S 1,2,4,19,63,153,1273,2090,19227,266133,868868,10631543,264365332,

%T 662822809,129102309125

%N Least k such that k(k+1)(k+2)(k+3) is divisible by prime(n)#.

%C Essentially indices of records in A053672.

%F Let p be the n-th prime, then (4p#)^(1/4) - 2 < a(n) < p#; in particular, a(n) >> exp(p/4).

%e 63 is in the sequence because {63, 64, 65, 66} are divisible by 2, 3, 5, 7, 11, and 13; no smaller number is divisible by all of these primes.

%o (PARI) a(n)=if(n<3,return(1));my(p=prime(n),P=prod(i=1,n-1,prime(i))/6, t=sqrtnint(24*p^2*P,4)+1); forstep(k=max(t\p,1)*p-3,P+2,[1,1,1,p-3], if(gcd(P, (k+3)*(k+2)*(k^2+k))==P,return(k)))

%Y Cf. A053672, A078638, A002110.

%K nonn,more

%O 2,2

%A _Charles R Greathouse IV_, Jun 20 2013

%E a(16) from _Charles R Greathouse IV_, Jun 21 2013

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Last modified November 15 14:23 EST 2018. Contains 317239 sequences. (Running on oeis4.)