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

1,1

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)

Links

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

Example

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).

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 *)

Crossrefs

Cf. A011371, A060818, A080765.

Sequence in context: A265790 A002540 A290515 * A045455 A160031 A154634

Adjacent sequences: A082090 A082091 A082092 * A082094 A082095 A082096

Keyword

nonn

Author

Labos Elemer, Apr 10 2003

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

Status

approved