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 sequence of terms together with their prime indices begins:
1: {} 25: {3,3} 43: {14} 62: {1,11}
3: {2} 26: {1,6} 44: {1,1,5} 63: {2,2,4}
5: {3} 27: {2,2,2} 45: {2,2,3} 65: {3,6}
7: {4} 28: {1,1,4} 46: {1,9} 66: {1,2,5}
9: {2,2} 29: {10} 47: {15} 67: {19}
10: {1,3} 30: {1,2,3} 49: {4,4} 68: {1,1,7}
11: {5} 31: {11} 50: {1,3,3} 69: {2,9}
13: {6} 33: {2,5} 51: {2,7} 70: {1,3,4}
14: {1,4} 34: {1,7} 52: {1,1,6} 71: {20}
15: {2,3} 35: {3,4} 53: {16} 73: {21}
17: {7} 37: {12} 55: {3,5} 74: {1,12}
19: {8} 38: {1,8} 57: {2,8} 75: {2,3,3}
21: {2,4} 39: {2,6} 58: {1,10} 76: {1,1,8}
22: {1,5} 41: {13} 59: {17} 77: {4,5}
23: {9} 42: {1,2,4} 61: {18} 78: {1,2,6}
For example, the prime indices of 45 are {2,2,3} with sum 7 >= 2*3, so 45 is in the sequence.
MATHEMATICA
Select[Range[100], PrimeOmega[#]<=Total[Cases[FactorInteger[#], {p_, k_}:>k*PrimePi[p]]]/2&]
CROSSREFS
The partitions with these Heinz numbers are counted by A110618.
The conjugate version is A322109.
The opposite version is A344296.
The conjugate opposite version is A344414.
The conjugate case of equality is A344415.
A001221 counts distinct prime indices.
A001222 counts prime indices with multiplicity.
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 15 2021
STATUS
approved