OFFSET
1,3
COMMENTS
EXAMPLE
The sequence of omega-sequences begins:
1: 26: 2 2 1 51: 2 2 1 76: 3 2 2 1
2: 1 27: 3 1 52: 3 2 2 1 77: 2 2 1
3: 1 28: 3 2 2 1 53: 1 78: 3 3 1
4: 2 1 29: 1 54: 4 2 2 1 79: 1
5: 1 30: 3 3 1 55: 2 2 1 80: 5 2 2 1
6: 2 2 1 31: 1 56: 4 2 2 1 81: 4 1
7: 1 32: 5 1 57: 2 2 1 82: 2 2 1
8: 3 1 33: 2 2 1 58: 2 2 1 83: 1
9: 2 1 34: 2 2 1 59: 1 84: 4 3 2 2 1
10: 2 2 1 35: 2 2 1 60: 4 3 2 2 1 85: 2 2 1
11: 1 36: 4 2 1 61: 1 86: 2 2 1
12: 3 2 2 1 37: 1 62: 2 2 1 87: 2 2 1
13: 1 38: 2 2 1 63: 3 2 2 1 88: 4 2 2 1
14: 2 2 1 39: 2 2 1 64: 6 1 89: 1
15: 2 2 1 40: 4 2 2 1 65: 2 2 1 90: 4 3 2 2 1
16: 4 1 41: 1 66: 3 3 1 91: 2 2 1
17: 1 42: 3 3 1 67: 1 92: 3 2 2 1
18: 3 2 2 1 43: 1 68: 3 2 2 1 93: 2 2 1
19: 1 44: 3 2 2 1 69: 2 2 1 94: 2 2 1
20: 3 2 2 1 45: 3 2 2 1 70: 3 3 1 95: 2 2 1
21: 2 2 1 46: 2 2 1 71: 1 96: 6 2 2 1
22: 2 2 1 47: 1 72: 5 2 2 1 97: 1
23: 1 48: 5 2 2 1 73: 1 98: 3 2 2 1
24: 4 2 2 1 49: 2 1 74: 2 2 1 99: 3 2 2 1
25: 2 1 50: 3 2 2 1 75: 3 2 2 1 100: 4 2 1
MATHEMATICA
red[n_]:=Times@@Prime/@Last/@If[n==1, {}, FactorInteger[n]];
omg[n_, k_]:=If[k==1, PrimeOmega[n], omg[red[n], k-1]];
dep[n_]:=If[n==1, 0, If[PrimeQ[n], 1, 1+dep[Times@@Prime/@Last/@If[n==1, {}, FactorInteger[n]]]]];
Table[omg[n, k], {n, 100}, {k, dep[n]}]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Jan 02 2019
STATUS
approved