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A332831
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Numbers whose unsorted prime signature is neither weakly increasing nor weakly decreasing.
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16
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90, 126, 198, 234, 270, 300, 306, 342, 350, 378, 414, 522, 525, 540, 550, 558, 588, 594, 600, 630, 650, 666, 702, 738, 756, 774, 810, 825, 846, 850, 918, 950, 954, 975, 980, 990, 1026, 1050, 1062, 1078, 1098, 1134, 1150, 1170, 1176, 1188, 1200, 1206, 1242
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OFFSET
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1,1
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COMMENTS
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A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization.
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LINKS
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FORMULA
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EXAMPLE
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The sequence of terms together with their prime indices begins:
90: {1,2,2,3}
126: {1,2,2,4}
198: {1,2,2,5}
234: {1,2,2,6}
270: {1,2,2,2,3}
300: {1,1,2,3,3}
306: {1,2,2,7}
342: {1,2,2,8}
350: {1,3,3,4}
378: {1,2,2,2,4}
414: {1,2,2,9}
522: {1,2,2,10}
525: {2,3,3,4}
540: {1,1,2,2,2,3}
550: {1,3,3,5}
558: {1,2,2,11}
588: {1,1,2,4,4}
594: {1,2,2,2,5}
600: {1,1,1,2,3,3}
630: {1,2,2,3,4}
For example, the prime signature of 540 is (2,3,1), so 540 is in the sequence.
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MATHEMATICA
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Select[Range[1000], !Or[LessEqual@@Last/@FactorInteger[#], GreaterEqual@@Last/@FactorInteger[#]]&]
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CROSSREFS
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The version for run-lengths of partitions is A332641.
The version for run-lengths of compositions is A332833.
The version for compositions is A332834.
Partitions with weakly increasing run-lengths are A100883.
Partitions with weakly increasing or decreasing run-lengths are A332745.
Compositions with weakly increasing or decreasing run-lengths are A332835.
Compositions with weakly increasing run-lengths are A332836.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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