OFFSET
2,6
COMMENTS
If the prime signature of n (nonincreasing version) is viewed as a partition, row n gives the conjugate partition.
EXAMPLE
24 = 2^3*3 is divisible by two prime numbers (2 and 3), one square of a prime (4 = 2^2), and one cube of a prime (8 = 2^3); therefore, row 24 of the table is {2,1,1}.
From Gus Wiseman, Mar 31 2022: (Start)
Rows begin:
1: () 16: (1,1,1,1) 31: (1)
2: (1) 17: (1) 32: (1,1,1,1,1)
3: (1) 18: (2,1) 33: (2)
4: (1,1) 19: (1) 34: (2)
5: (1) 20: (2,1) 35: (2)
6: (2) 21: (2) 36: (2,2)
7: (1) 22: (2) 37: (1)
8: (1,1,1) 23: (1) 38: (2)
9: (1,1) 24: (2,1,1) 39: (2)
10: (2) 25: (1,1) 40: (2,1,1)
11: (1) 26: (2) 41: (1)
12: (2,1) 27: (1,1,1) 42: (3)
13: (1) 28: (2,1) 43: (1)
14: (2) 29: (1) 44: (2,1)
15: (2) 30: (3) 45: (2,1)
(End)
MATHEMATICA
Table[Length/@Table[Select[Last/@FactorInteger[n], #>=k&], {k, Max@@Last/@FactorInteger[n]}], {n, 2, 100}] (* Gus Wiseman, Mar 31 2022 *)
KEYWORD
nonn,tabf
AUTHOR
Matthew Vandermast, Apr 28 2014
STATUS
approved