|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,2
|
|
COMMENTS
|
Essentially indices of records in A053672.
|
|
LINKS
|
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|