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Search: id:A134459
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| A134459 |
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Numbers n such that lcm(1..(n-1))<lcm(1..n)<lcm(1..(n+1)). |
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+0
2
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| 2, 3, 4, 7, 16, 31, 127, 256, 8191, 65536, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727
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OFFSET
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1,1
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COMMENT
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1. Or, numbers n such that A003418(n-1)<A003418(n)<A003418(n+1). Sequence is the union(A019434 - 1, A000668) - Zak Seidov. 2. lcm(1..n-1) < lcm(1..n) iff n is a prime power. So the sequence consists of those n for which both n and n+1 are prime powers. By Catalan's conjecture (proved by Mihailescu), the only case where n and n+1 are both powers > 1 is n=8. Otherwise, whichever of n and n+1 is even must be a power of 2 and the other must be a prime: either a Mersenne prime if n+1 is the power of 2, or a Fermat prime if n is the power of 2. - Robert Israel (israel(AT)math.ubc.ca).
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CROSSREFS
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Cf. A000668, A003418, A019434. Essentially a duplicate of A068194.
Sequence in context: A091155 A027362 A068194 this_sequence A110705 A139439 A119330
Adjacent sequences: A134456 A134457 A134458 this_sequence A134460 A134461 A134462
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Jan 18 2008
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