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.

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

Author

Amarnath Murthy, Sep 20 2002

Keywords

• nonn
• easy

Examples

			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
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..2236

Crossrefs

Cf. A075365, A075366, A075367.

Programs

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]]

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

Formula

a(n) = A075367(n)/A034386(n).

Extensions

Edited by Dean Hickerson, Oct 28 2002