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

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

Offset

1,1

Comments

A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization.

Links

Table of n, a(n) for n=1..49.

Formula

Intersection of A071365 and A112769.

Example

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.

Mathematica

Select[Range[1000], !Or[LessEqual@@Last/@FactorInteger[#], GreaterEqual@@Last/@FactorInteger[#]]&]

Crossrefs

The version for run-lengths of partitions is A332641.

The version for run-lengths of compositions is A332833.

The version for compositions is A332834.

Prime signature is A124010.

Unimodal compositions are A001523.

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.

Cf. A100882, A115981, A328509, A329398, A332281, A332640, A332643, A332746, A332836, A332870.

Sequence in context: A114826 A332725 A253385 * A103653 A332642 A352231

Adjacent sequences: A332828 A332829 A332830 * A332832 A332833 A332834

Keyword

nonn

Author

Gus Wiseman, Mar 02 2020

Status

approved