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A075368
Smallest integer value of lcm(n+1, n+2, ..., n+k) (for k >= 0) divided by the product of all the primes up to n.
4
1, 6, 10, 5, 84, 84, 1716, 858, 286, 286, 100776, 100776, 891480, 891480, 891480, 445740, 282861360, 282861360, 550835280, 550835280, 550835280, 550835280, 42222721680, 42222721680, 8444544336, 8444544336, 2814848112, 2814848112
OFFSET
1,2
LINKS
FORMULA
a(n) = A075367(n)/A034386(n).
EXAMPLE
a(3) = 10 as the product of primes <= (n = 3) is 6 and the smallest integer of the form lcm(3+1, 3+2, ..., 3+k) = lcm(4, 5, 6) = 60 giving a(3) = 60/6 = 10. - David A. Corneth, Dec 05 2023
MATHEMATICA
a75365[n_] := Module[{div, k, pr}, div=Times@@Prime/@Range[PrimePi[n]]; For[k=0; pr=1, True, k++; pr*=n+k, If[Mod[pr, div]==0, Return[k]]]]; a[1]=1; a[n_] := LCM@@Range[n+1, n+a75365[n]]/Times@@Prime/@Range[PrimePi[n]]
PROG
(PARI)
a(n) = {if(n==1, return(1));
my(pp = vecprod(primes(primepi(n))), l = n+1);
for(k = n+2, 2*n,
l = lcm(l, k);
if(l%pp == 0,
return(l\pp)
)
)
} \\ David A. Corneth, Dec 05 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy, Sep 20 2002
EXTENSIONS
Edited by Dean Hickerson, Oct 28 2002
STATUS
approved