A348123 Starts of runs of 3 consecutive numbers that have more nonunitary than unitary prime divisors (A348121).

959075, 1492775, 5038523, 5132699, 9905300, 38002831, 40441023, 50473575, 67706631, 80108775, 81355923, 109436875, 128428999, 165332223, 169067491, 171024111, 178878175, 196224075, 224042624, 247529574, 274205223, 279645399, 282880575, 284267374, 299969423, 329523775

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

Subsequence of A348121 and A348122.

Cf. A001694.

Similar sequence: A348120.

Sequence in context: A341897 A341898 A092377 * A022236 A083609 A093216

Adjacent sequences: A348120 A348121 A348122 * A348124 A348125 A348126

Keyword

nonn

Author

Amiram Eldar, Oct 01 2021

Status

approved