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URL: https://oeis.org/A226891

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A226891
Least k such that k(k+1)(k+2)(k+3) is divisible by prime(n)#.
1
1, 2, 4, 19, 63, 153, 1273, 2090, 19227, 266133, 868868, 10631543, 264365332, 662822809, 129102309125
OFFSET
2,2
COMMENTS
Essentially indices of records in A053672.
FORMULA
Let p be the n-th prime, then (4p#)^(1/4) - 2 < a(n) < p#; in particular, a(n) >> exp(p/4).
EXAMPLE
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.
PROG
(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)))
CROSSREFS
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
a(16) from Charles R Greathouse IV, Jun 21 2013
STATUS
approved