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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
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
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
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