OFFSET
1,1
COMMENTS
A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization.
Also nonsquarefree numbers whose prime factors, taken in order and with multiplicity, are alternately constant and weakly increasing, starting with either.
Also the Heinz numbers of non-strict integer partitions whose part multiplicities, except possibly the first and last, are all even. These are counted by A349795.
EXAMPLE
The terms together with their prime indices begin:
4: {1,1}
8: {1,1,1}
9: {2,2}
12: {1,1,2}
16: {1,1,1,1}
18: {1,2,2}
20: {1,1,3}
24: {1,1,1,2}
25: {3,3}
27: {2,2,2}
28: {1,1,4}
32: {1,1,1,1,1}
36: {1,1,2,2}
40: {1,1,1,3}
44: {1,1,5}
45: {2,2,3}
48: {1,1,1,1,2}
MATHEMATICA
Select[Range[100], !SquareFreeQ[#]&&(PrimePowerQ[#]||And@@EvenQ/@Take[Last/@FactorInteger[#], {2, -2}])&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 23 2021
STATUS
approved