OFFSET
1,1
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. 1 has no prime indices so is not included.
EXAMPLE
The sequence of terms together with their prime indices begins:
2: {1} 24: {1,1,1,2} 46: {1,9}
4: {1,1} 25: {3,3} 47: {15}
5: {3} 26: {1,6} 48: {1,1,1,1,2}
6: {1,2} 28: {1,1,4} 50: {1,3,3}
8: {1,1,1} 30: {1,2,3} 52: {1,1,6}
10: {1,3} 31: {11} 54: {1,2,2,2}
11: {5} 32: {1,1,1,1,1} 55: {3,5}
12: {1,1,2} 34: {1,7} 56: {1,1,1,4}
14: {1,4} 35: {3,4} 58: {1,10}
16: {1,1,1,1} 36: {1,1,2,2} 59: {17}
17: {7} 38: {1,8} 60: {1,1,2,3}
18: {1,2,2} 40: {1,1,1,3} 62: {1,11}
20: {1,1,3} 41: {13} 64: {1,1,1,1,1,1}
22: {1,5} 42: {1,2,4} 65: {3,6}
23: {9} 44: {1,1,5} 66: {1,2,5}
MATHEMATICA
Select[Range[100], OddQ[PrimePi[FactorInteger[#][[1, 1]]]]&]
CROSSREFS
These partitions are counted by A026804.
The case where all prime indices are odd is A066208.
Looking at greatest prime index instead of least gives A244991.
A001222 counts prime factors.
A005408 lists odd numbers.
A031368 lists odd-indexed primes.
A055396 selects least prime index.
A056239 adds up prime indices.
A061395 selects greatest prime index.
A112798 lists the prime indices of each positive integer.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 12 2021
STATUS
approved