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