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A082093 a(n) is the least number m such that (m+n)!/m! = (m+1)*(m+2)*...*(m+n) divides lcm(1,...,m). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 22 10:24 EDT 2019. Contains 328317 sequences. (Running on oeis4.)