A348120 -id:A348120 - cp's OEIS frontend

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

Amiram Eldar, Oct 01 2021

nonn

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.

			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.

Amiram Eldar, Table of n, a(n) for n = 1..500

Subsequence of A348121 and A348122.
Cf. A001694.
Similar sequence: A348120.

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

cp's OEIS Frontend

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

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