OFFSET
1,2
COMMENTS
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
EXAMPLE
The prime indices of 105 are {2,3,4}, and there are 3 prime factors (3,5,7) and 4 distinct divisors of prime indices (1,2,3,4), so 105 is in the sequence.
The terms together with their prime indices begin:
1: {} 22: {1,5} 42: {1,2,4} 63: {2,2,4}
2: {1} 23: {9} 43: {14} 65: {3,6}
3: {2} 25: {3,3} 45: {2,2,3} 66: {1,2,5}
5: {3} 26: {1,6} 46: {1,9} 67: {19}
6: {1,2} 28: {1,1,4} 47: {15} 69: {2,9}
7: {4} 29: {10} 49: {4,4} 70: {1,3,4}
9: {2,2} 30: {1,2,3} 51: {2,7} 71: {20}
10: {1,3} 31: {11} 52: {1,1,6} 73: {21}
11: {5} 33: {2,5} 53: {16} 74: {1,12}
13: {6} 34: {1,7} 55: {3,5} 75: {2,3,3}
14: {1,4} 35: {3,4} 57: {2,8} 76: {1,1,8}
15: {2,3} 37: {12} 58: {1,10} 77: {4,5}
17: {7} 38: {1,8} 59: {17} 78: {1,2,6}
19: {8} 39: {2,6} 61: {18} 79: {22}
21: {2,4} 41: {13} 62: {1,11} 82: {1,13}
MATHEMATICA
Select[Range[100], PrimeOmega[#]<=Length[Union @@ Divisors/@PrimePi/@First/@If[#==1, {}, FactorInteger[#]]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 16 2024
STATUS
approved