OFFSET
1,1
COMMENTS
First differs from A299117 in having 150.
An anti-run is a sequence with no adjacent equal terms. The maxima of maximal anti-runs in a sequence are obtained by splitting it into maximal anti-run subsequences and taking the greatest term of each.
The partitions with these Heinz numbers are those with (1) some part appearing more than twice or (2) the greatest part appearing more than once.
Note the prime factors can alternatively be written in weakly decreasing order.
EXAMPLE
The maximal anti-runs of prime factors of 150 are ((2,3,5),(5)), with maxima (5,5), so 150 is in the sequence.
The maximal anti-runs of prime factors of 180 are ((2),(2,3),(3,5)), with maxima (2,3,5), so 180 is not in the sequence.
The maximal anti-runs of prime factors of 300 are ((2),(2,3,5),(5)), with maxima (2,5,5), so 300 is in the sequence.
The terms together with their prime indices begin:
4: {1,1}
8: {1,1,1}
9: {2,2}
16: {1,1,1,1}
18: {1,2,2}
24: {1,1,1,2}
25: {3,3}
27: {2,2,2}
32: {1,1,1,1,1}
36: {1,1,2,2}
40: {1,1,1,3}
48: {1,1,1,1,2}
MATHEMATICA
Select[Range[150], !UnsameQ@@Max /@ Split[Flatten[ConstantArray@@@FactorInteger[#]], UnsameQ]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 15 2024
STATUS
approved