cp's OEIS Frontend

A332831 Numbers whose unsorted prime signature is neither weakly increasing nor weakly decreasing.

%I A332831 #9 Mar 02 2020 18:54:45
%S A332831 90,126,198,234,270,300,306,342,350,378,414,522,525,540,550,558,588,
%T A332831 594,600,630,650,666,702,738,756,774,810,825,846,850,918,950,954,975,
%U A332831 980,990,1026,1050,1062,1078,1098,1134,1150,1170,1176,1188,1200,1206,1242
%N A332831 Numbers whose unsorted prime signature is neither weakly increasing nor weakly decreasing.
%C A332831 A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization.
%F A332831 Intersection of A071365 and A112769.
%e A332831 The sequence of terms together with their prime indices begins:
%e A332831    90: {1,2,2,3}
%e A332831   126: {1,2,2,4}
%e A332831   198: {1,2,2,5}
%e A332831   234: {1,2,2,6}
%e A332831   270: {1,2,2,2,3}
%e A332831   300: {1,1,2,3,3}
%e A332831   306: {1,2,2,7}
%e A332831   342: {1,2,2,8}
%e A332831   350: {1,3,3,4}
%e A332831   378: {1,2,2,2,4}
%e A332831   414: {1,2,2,9}
%e A332831   522: {1,2,2,10}
%e A332831   525: {2,3,3,4}
%e A332831   540: {1,1,2,2,2,3}
%e A332831   550: {1,3,3,5}
%e A332831   558: {1,2,2,11}
%e A332831   588: {1,1,2,4,4}
%e A332831   594: {1,2,2,2,5}
%e A332831   600: {1,1,1,2,3,3}
%e A332831   630: {1,2,2,3,4}
%e A332831 For example, the prime signature of 540 is (2,3,1), so 540 is in the sequence.
%t A332831 Select[Range[1000],!Or[LessEqual@@Last/@FactorInteger[#],GreaterEqual@@Last/@FactorInteger[#]]&]
%Y A332831 The version for run-lengths of partitions is A332641.
%Y A332831 The version for run-lengths of compositions is A332833.
%Y A332831 The version for compositions is A332834.
%Y A332831 Prime signature is A124010.
%Y A332831 Unimodal compositions are A001523.
%Y A332831 Partitions with weakly increasing run-lengths are A100883.
%Y A332831 Partitions with weakly increasing or decreasing run-lengths are A332745.
%Y A332831 Compositions with weakly increasing or decreasing run-lengths are A332835.
%Y A332831 Compositions with weakly increasing run-lengths are A332836.
%Y A332831 Cf. A100882, A115981, A328509, A329398, A332281, A332640, A332643, A332746, A332836, A332870.
%K A332831 nonn
%O A332831 1,1
%A A332831 _Gus Wiseman_, Mar 02 2020