A348099 Starts of runs of 3 consecutive numbers that have an equal number of unitary and nonunitary prime divisors (A348097).

423, 603, 1250, 1375, 2007, 2523, 2527, 3175, 4075, 4203, 4374, 4923, 4948, 7442, 8991, 10375, 10467, 12591, 18027, 20402, 20575, 22023, 22687, 23823, 26071, 28375, 30231, 31507, 31850, 33271, 34623, 35574, 36162, 37348, 40023, 49975, 50274, 54475, 54511, 55323

Offset: 1

Author

Amiram Eldar, Sep 30 2021

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A348097 and A348098.

Cf. A335397.

Programs

Mathematica

q[n_] := n == 1 || Count[(e = FactorInteger[n][[;; , 2]]), 1] == Length[e]/2; v = q /@ Range[3]; seq = {}; Do[v = Append[Drop[v, 1], q[k]]; If[And @@ v, AppendTo[seq, k - 2]], {k, 4, 10^5}]; seq

Formula

423 is a term since 423 = 3^2 * 47, 423 + 1 = 424 = 2^3 * 53 and 423 + 2 = 425 = 5^2 * 17 all have one unitary prime divisor and one nonunitary prime divisor.