OFFSET
1,2
COMMENTS
The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.
EXAMPLE
The terms together with their corresponding compositions begin:
1: (1)
2: (2)
3: (1,1)
4: (3)
7: (1,1,1)
8: (4)
10: (2,2)
15: (1,1,1,1)
16: (5)
17: (4,1)
24: (1,4)
31: (1,1,1,1,1)
32: (6)
36: (3,3)
42: (2,2,2)
63: (1,1,1,1,1,1)
64: (7)
69: (4,2,1)
MATHEMATICA
stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Select[Range[0, 1000], IntegerQ[GeometricMean[stc[#]]]&]
CROSSREFS
Subsets whose geometric mean is an integer are counted by A326027.
These compositions are counted by A357710.
A078175 lists numbers whose prime factors have integer average.
A320322 counts partitions whose product is a perfect power.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 16 2022
STATUS
approved