A348123 - OEIS

%I #9 Oct 03 2021 08:10:20

%S 959075,1492775,5038523,5132699,9905300,38002831,40441023,50473575,

%T 67706631,80108775,81355923,109436875,128428999,165332223,169067491,

%U 171024111,178878175,196224075,224042624,247529574,274205223,279645399,282880575,284267374,299969423,329523775

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

%C There are no runs of 4 consecutive numbers below 2.4*10^10.

%C 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.

%H Amiram Eldar, <a href="/A348123/b348123.txt">Table of n, a(n) for n = 1..500</a>

%e 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.

%t 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

%Y Subsequence of A348121 and A348122.

%Y Cf. A001694.

%Y Similar sequence: A348120.

%K nonn

%O 1,1

%A _Amiram Eldar_, Oct 01 2021