OFFSET
1,1
COMMENTS
Equally, numbers n for which A061395(n) is odd.
If the Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), these are the Heinz numbers of partitions whose greatest part is odd, counted by A027193. - Gus Wiseman, Feb 08 2021
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10001
FORMULA
For all n, A244989(a(n)) = n.
EXAMPLE
From Gus Wiseman, Feb 08 2021: (Start)
The sequence of terms together with their prime indices begins:
2: {1} 32: {1,1,1,1,1} 64: {1,1,1,1,1,1}
4: {1,1} 33: {2,5} 66: {1,2,5}
5: {3} 34: {1,7} 67: {19}
8: {1,1,1} 40: {1,1,1,3} 68: {1,1,7}
10: {1,3} 41: {13} 69: {2,9}
11: {5} 44: {1,1,5} 73: {21}
15: {2,3} 45: {2,2,3} 75: {2,3,3}
16: {1,1,1,1} 46: {1,9} 77: {4,5}
17: {7} 47: {15} 80: {1,1,1,1,3}
20: {1,1,3} 50: {1,3,3} 82: {1,13}
22: {1,5} 51: {2,7} 83: {23}
23: {9} 55: {3,5} 85: {3,7}
25: {3,3} 59: {17} 88: {1,1,1,5}
30: {1,2,3} 60: {1,1,2,3} 90: {1,2,2,3}
31: {11} 62: {1,11} 92: {1,1,9}
(End)
MATHEMATICA
Select[Range[100], OddQ[PrimePi[FactorInteger[#][[-1, 1]]]]&] (* Gus Wiseman, Feb 08 2021 *)
PROG
CROSSREFS
Complement: A244990.
Looking at least instead of greatest prime index gives A026804.
The partitions with these Heinz numbers are counted by A027193.
The case where Omega is odd also is A340386.
A001222 counts prime factors.
A056239 adds up prime indices.
A300063 ranks partitions of odd numbers.
A061395 selects maximum prime index.
A066208 ranks partitions into odd parts.
A112798 lists the prime indices of each positive integer.
A340931 ranks odd-length partitions of odd numbers.
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 21 2014
STATUS
approved