A275120 List the least common multiples of {1, 2, ..., k} for k = 0, 1, ...; this sequence gives the length of the n-th block of consecutive equal numbers.

2, 1, 1, 1, 2, 1, 1, 2, 2, 3, 1, 2, 4, 2, 2, 2, 2, 1, 5, 4, 2, 4, 2, 4, 6, 2, 3, 3, 4, 2, 6, 2, 2, 6, 8, 4, 2, 4, 2, 4, 8, 4, 2, 1, 3, 6, 2, 10, 2, 6, 6, 4, 2, 4, 6, 2, 10, 2, 4, 2, 12, 12, 4, 2, 4, 6, 2, 2, 8, 5, 1, 6, 6, 2, 6, 4, 2, 6, 4, 14, 4, 2, 4, 14, 6, 6, 4, 2, 4, 6, 2, 6, 6, 6, 4, 6

Offset

1,1

Comments

a(n) is the count of how many consecutive terms in A003418 are equal.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) = A057820(n), n>1.

Example

lcm({}) = lcm({1}) = 1, so a(1) = 2.
lcm({1, 2}) = 2, so a(2) = 1.
lcm({1, 2, 3}) = 6, so a(3) = 1.
lcm({1, 2, 3, 4}) = 12, so a(4) = 1.
lcm({1, ..., 5}) = lcm({1, ..., 6}) = 60, so a(5) = 2.
lcm({1, ..., 7}) = 420, so a(6) = 1.
lcm({1, ..., 8}) = 840, so a(7) = 1.
lcm({1, ..., 9}) = lcm({1, ..., 10}) = 2520, so a(8) = 2.
lcm({1, ..., 11}) = lcm({1, ..., 12}) = 27720, so a(9) = 2.

Mathematica

{2}~Join~Rest@ Most@ Map[Length, Split@ Table[LCM @@ Range@ n, {n, 396}]] (* Michael De Vlieger, Jul 18 2016 *)

Prog

(PARI) do(lim)=my(v=List()); for(e=2, logint(lim\=1, 2), forprime(p=2, sqrtnint(lim, e), listput(v, p^e))); v=Set(concat(Vec(v), primes([2, lim]))); concat(2, vector(#v-1, i, v[i+1]-v[i])) \\ Charles R Greathouse IV, Jul 18 2016

Crossrefs

Frequency of given numbers using A003418.

Apart from the first term, same as A057820.

Sequence in context: A029444 A122191 A097847 * A144379 A337260 A296772

Adjacent sequences: A275117 A275118 A275119 * A275121 A275122 A275123

Keyword

nonn

Author

Tyler Skywalker, Jul 18 2016

Status

approved