A328189 - OEIS

%I #9 Mar 14 2023 15:52:39

%S 8,16,18,20,27,28,32,40,42,44,50,52,54,56,64,66,68,75,76,78,80,81,88,

%T 92,98,99,100,102,104,110,112,114,116,117,124,125,126,128,130,136,138,

%U 140,147,148,152,153,156,160,162,164,170,171,172,174,176,184,186

%N Numbers n with at least one pair of consecutive divisible nontrivial divisors (greater than 1 and less than n).

%e The nontrivial divisors of 42 are {2, 3, 6, 7, 14, 21}, with pairs of consecutive divisible divisors {3, 6} and {7, 14}, so 42 belongs to the sequence.

%t Select[Range[200],MatchQ[DeleteCases[Divisors[#],1|#],{___,x_,y_,___}/;Divisible[y,x]]&]

%t Select[Range[2,200],AnyTrue[Partition[Most[Rest[Divisors[#]]],2,1],Mod[#[[2]],#[[1]]] == 0&]&] (* _Harvey P. Dale_, Mar 14 2023 *)

%Y Complement of A328161.

%Y Positions of terms greater than 1 in A328194.

%Y Partitions with a pair of consecutive divisible parts are A328221.

%Y Cf. A000005, A060680, A060775, A067513, A088725, A163870, A328028, A328162, A328171.

%K nonn

%O 1,1

%A _Gus Wiseman_, Oct 13 2019