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

1,2

Links

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

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

Cf. A075365, A075366, A075367.

Sequence in context: A083478 A328202 A306368 * A235117 A339590 A074288

Adjacent sequences: A075365 A075366 A075367 * A075369 A075370 A075371

Keyword

nonn,easy

Author

Amarnath Murthy, Sep 20 2002

Extensions

Edited by Dean Hickerson, Oct 28 2002

Status

approved