OFFSET
1,1
COMMENTS
Also Heinz numbers of strict integer partitions whose greatest part is divisible by their number of parts. These partitions are counted by A340828.
EXAMPLE
The sequence of terms together with their prime indices begins:
2: {1} 31: {11} 71: {20}
3: {2} 35: {3,4} 73: {21}
5: {3} 37: {12} 74: {1,12}
6: {1,2} 38: {1,8} 78: {1,2,6}
7: {4} 39: {2,6} 79: {22}
11: {5} 41: {13} 83: {23}
13: {6} 43: {14} 86: {1,14}
14: {1,4} 47: {15} 87: {2,10}
17: {7} 53: {16} 89: {24}
19: {8} 57: {2,8} 91: {4,6}
21: {2,4} 58: {1,10} 95: {3,8}
23: {9} 59: {17} 97: {25}
26: {1,6} 61: {18} 101: {26}
29: {10} 65: {3,6} 103: {27}
30: {1,2,3} 67: {19} 106: {1,16}
MATHEMATICA
Select[Range[2, 100], SquareFreeQ[#]&&Divisible[PrimePi[FactorInteger[#][[-1, 1]]], PrimeOmega[#]]&]
CROSSREFS
Note: Heinz number sequences are given in parentheses below.
The case of equality, and the reciprocal version, are both A002110.
These are the Heinz numbers of partitions counted by A340828.
A001222 counts prime factors.
A056239 adds up the prime indices.
A061395 selects the maximum prime index.
A112798 lists the prime indices of each positive integer.
A257541 gives the rank of the partition with Heinz number n.
A340830 counts strict partitions whose parts are multiples of the length.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 05 2021
STATUS
approved