OFFSET
1,1
COMMENTS
There are no runs of 4 consecutive numbers below 2.4*10^10.
It is conjectured that there are no runs of 3 consecutive numbers that are powerful (A001694), but if they do exist, their starts are contained in this sequence.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..500
EXAMPLE
959075 is a term since 959075 = 5^2 * 13^2 * 227, 959075 + 1 = 959076 = 2^2 * 3^2 * 26641 and 959075 + 2 = 959077 = 7^2 * 23^2 * 37 all have 2 nonunitary prime divisors and only 1 unitary prime divisor.
MATHEMATICA
q[n_] := 2*Count[(e = FactorInteger[n][[;; , 2]]), 1] < Length[e]; v = q /@ Range[3]; seq = {}; Do[v = Append[Drop[v, 1], q[k]]; If[And @@ v, AppendTo[seq, k - 2]], {k, 4, 5*10^7}]; seq
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 01 2021
STATUS
approved