%I #39 Nov 05 2023 22:05:17

%S 5,9,10,11,12,14,15,17,18,22,23,24,25,26,27,30,31,32,36,46,47,48,52,

%T 62,71,72,79,80,81,96,106,107,126,127,162,191,192,241,242,256,382,431,

%U 486,512,576,862,1151,1152,2186,2591,2592,2916,4372,8191,8746,131071,131072,139967,472391,524287,786431,995326,995327

%N Numbers k such that k*(k+1)*(k+2) has exactly 4 distinct prime factors.

%C Contains 2^p-1 for p in A107360 except 3.

%C Contains all terms of A325255 except 2 and 4.

%C Contains k-1 for k in A027856 except 4.

%C Contains k-2 for k in A327240 except 6 and 8. - _Ray Chandler_, Sep 14 2019

%H Ray Chandler, <a href="/A325204/b325204.txt">Table of n, a(n) for n = 1..178</a> (terms < 10^1000; first 114 terms from Robert Israel)

%H Ray Chandler, <a href="/A325204/a325204.txt">Mathematica code used to compute b-file</a>.

%H Math StackExchange, <a href="https://math.stackexchange.com/questions/3345481/three-consecutive-numbers-with-exactly-different-four-prime-factors#comment6886521_3345481">Three consecutive numbers with exactly different four prime factors</a>.

%e a(3)=10 is in the sequence because 10*11*12 has four distinct prime factors: 2, 3, 5, 11.

%p select(t -> nops(numtheory:-factorset(t) union numtheory:-factorset(t+1) union numtheory:-factorset(t+2))=4, [$1..10^6]);

%o (PARI) select(k->4==omega(k*(k+1)*(k+2)), [1..10000]) \\ _Andrew Howroyd_, Sep 05 2019

%Y Cf. A027856, A107360, A325255, A327240.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Sep 05 2019