A342030 Starts of runs of 4 consecutive numbers that have mutually distinct exponents in their prime factorization (A130091).

1, 2, 16, 17, 47, 96, 241, 242, 575, 1249, 2644, 2645, 4049, 4372, 4373, 4799, 9124, 12248, 33749, 72250, 120049, 130436, 281249, 303748, 1431124, 1431125, 1531250, 2101247, 3693761, 4085656, 4910975, 12502348, 12502349, 14268481, 22997761, 25486324, 26693549

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..196 (terms below 10^11)

Kevser Aktaş and M. Ram Murty, On the number of special numbers, Proceedings - Mathematical Sciences, Vol. 127, No. 3 (2017), pp. 423-430; alternative link.

Bernardo Recamán Santos, Consecutive numbers with mutually distinct exponents in their canonical prime factorization, MathOverflow, Mar 30 2015.

Example

2 is a term since 2, 3, 4 = 2^2, and 5 all have a single exponent in their prime factorization.
3 is not a term since in the run {3, 4, 5, 6} the fourth member 6 = 2*3 has two equal exponents (1) in its prime factorization.

Mathematica

q[n_] := Length[(e = FactorInteger[n][[;; , 2]])] == Length[Union[e]]; v = q /@ Range[4]; seq = {}; Do[If[And @@ v, AppendTo[seq, k - 4]]; v = Join[Rest[v], {q[k]}], {k, 5, 10^5}]; seq

Crossrefs

Subsequence of A130091, A342028 and A342029.

A342031 is a subsequence.

Sequence in context: A075376 A032935 A004831 * A368404 A217307 A282408

Adjacent sequences: A342027 A342028 A342029 * A342031 A342032 A342033

Keyword

nonn

Author

Amiram Eldar, Feb 25 2021

Status

approved