A082093 a(n) is the least number m such that (m+n)!/m! = (m+1)*(m+2)*...*(m+n) divides lcm(1,...,m).

5, 13, 19, 32, 73, 89, 140, 199, 294, 468, 1072, 1072, 1072, 2161, 2976, 32805, 32806, 65732, 65732, 262153, 262154, 524457, 524640, 4194464, 4194464, 8388640, 8388640, 33554432, 33554432, 67108992, 67109088, 2147483659, 2147484110, 4294967312, 4294967312, 17179869209, 17179869210

Offset: 1

Author

Labos Elemer, Apr 10 2003

Keywords

• nonn

Comments

From David A. Corneth, Aug 30 2019: (Start)

As (m+1)*(m+2)*...*(m+n) is the product of n consecutive integers, it's divisible by n! and so a(n) >= 2^A011371(n) = A060818(n).

None of m+1..m+n are prime. (End)

Examples

			a(6)=89: lcm(1,...,89) = 718766754945489455304472257065075294400 is divisible by 625757605200 = 90*91*92*93*94*95 = (89+6)!/89! and the quotient is 1148634469597477063638686172.
For n=1 see A080765(1) = A082093(1).
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..75

Crossrefs

Cf. A011371, A060818, A080765.

Programs

Mathematica

k = 1; lc = 1; Do[While[lc = LCM[lc, k]; Mod[lc, (n + k)!/k! ] != 0, k++ ]; Print[{n, k}], {n, 0, 50}] (* Robert G. Wilson v, Apr 12 2006 *)

Extensions

a(16)-a(19) from Robert G. Wilson v, Apr 12 2006

a(20)-a(23) from Vaclav Kotesovec, Aug 30 2019

a(24)-a(37) from David A. Corneth, Aug 30 2019