cp's OEIS Frontend

A329140 Numbers whose prime signature is a periodic word.

%I A329140 #4 Nov 10 2019 20:29:19
%S A329140 6,10,14,15,21,22,26,30,33,34,35,36,38,39,42,46,51,55,57,58,62,65,66,
%T A329140 69,70,74,77,78,82,85,86,87,91,93,94,95,100,102,105,106,110,111,114,
%U A329140 115,118,119,122,123,129,130,133,134,138,141,142,143,145,146,154
%N A329140 Numbers whose prime signature is a periodic word.
%C A329140 First differs from A182853 in having 2100 = 2^2 * 3^1 * 5^2 * 7^1.
%C A329140 A number's prime signature (A124010) is the sequence of positive exponents in its prime factorization.
%C A329140 A sequence is aperiodic if its cyclic rotations are all different.
%e A329140 The sequence of terms together with their prime signatures begins:
%e A329140    6: (1,1)
%e A329140   10: (1,1)
%e A329140   14: (1,1)
%e A329140   15: (1,1)
%e A329140   21: (1,1)
%e A329140   22: (1,1)
%e A329140   26: (1,1)
%e A329140   30: (1,1,1)
%e A329140   33: (1,1)
%e A329140   34: (1,1)
%e A329140   35: (1,1)
%e A329140   36: (2,2)
%e A329140   38: (1,1)
%e A329140   39: (1,1)
%e A329140   42: (1,1,1)
%e A329140   46: (1,1)
%e A329140   51: (1,1)
%e A329140   55: (1,1)
%e A329140   57: (1,1)
%e A329140   58: (1,1)
%t A329140 aperQ[q_]:=Array[RotateRight[q,#1]&,Length[q],1,UnsameQ];
%t A329140 Select[Range[100],!aperQ[Last/@FactorInteger[#]]&]
%Y A329140 Complement of A329139.
%Y A329140 Periodic compositions are A178472.
%Y A329140 Periodic binary words are A152061.
%Y A329140 Numbers whose binary expansion is periodic are A121016.
%Y A329140 Numbers whose prime signature is a Lyndon word are A329131.
%Y A329140 Numbers whose prime signature is a necklace are A329138.
%Y A329140 Cf. A025487, A056239, A097318, A112798, A118914, A124010, A181819, A304678, A329132 A329134, A329143, A329144.
%K A329140 nonn
%O A329140 1,1
%A A329140 _Gus Wiseman_, Nov 09 2019