%I #41 Jul 29 2023 14:06:39

%S 14,20,21,33,34,35,38,39,44,45,50,51,54,55,56,57,62,68,74,75,76,85,86,

%T 87,91,92,93,94,95,98,99,111,115,116,117,118,122,123,133,134,135,141,

%U 142,143,144,145,146,147,152,158,159,160,161,171,175,176,177,183,184

%N Numbers k such that k and k+1 both have exactly 2 distinct prime factors.

%C Subsequence of A006049. - _Michel Marcus_, May 06 2016

%H Seiichi Manyama, <a href="/A074851/b074851.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) seems to be asymptotic to c*n*log(n)^2 with c=0.13...

%F {k: A001221(k) = A001221(k+1) = 2}. - _R. J. Mathar_, Jul 18 2023

%e 20=2^2*5 21=3*7 hence 20 is in the sequence.

%t Flatten[Position[Partition[Table[If[PrimeNu[n]==2,1,0],{n,200}],2,1],{1,1}]] (* _Harvey P. Dale_, Mar 12 2015 *)

%o (PARI) isok(n) = (omega(n) == 2) && (omega(n+1) == 2); \\ _Michel Marcus_, May 06 2016

%o (Magma) [n: n in [2..200] | #PrimeDivisors(n) eq 2 and #PrimeDivisors(n+1) eq 2]; // _Vincenzo Librandi_, Dec 05 2018

%o (GAP) Filtered([1..200],n->[Size(Set(Factors(n))),Size(Set(Factors(n+1)))]=[2,2]); # _Muniru A Asiru_, Dec 05 2018

%o (Python)

%o import sympy

%o from sympy.ntheory.factor_ import primenu

%o for n in range(1,200):

%o if primenu(n)==2 and primenu(n+1)==2:

%o print(n, end=', '); # _Stefano Spezia_, Dec 05 2018

%Y Cf. A006049, A006549, A001221.

%Y Analogous sequences for m distinct prime factors: this sequence (m=2), A140077 (m=3), A140078 (m=4), A140079 (m=5), A273879 (m=6).

%Y Cf. A093548.

%Y Equals A255346 \ A321502.

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, Sep 10 2002