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%I #11 Jun 21 2013 17:33:36
%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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