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A325706
Heinz numbers of integer partitions containing all of their distinct multiplicities.
7
1, 2, 6, 9, 10, 12, 14, 18, 22, 26, 30, 34, 36, 38, 40, 42, 46, 58, 60, 62, 66, 70, 74, 78, 82, 84, 86, 90, 94, 102, 106, 110, 112, 114, 118, 120, 122, 125, 126, 130, 132, 134, 138, 142, 146, 150, 154, 156, 158, 166, 170, 174, 178, 180, 182, 186, 190, 194, 198
OFFSET
1,2
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
Also numbers n divisible by the squarefree kernel of their "shadow" A181819(n).
The enumeration of these partitions by sum is given by A325705.
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
6: {1,2}
9: {2,2}
10: {1,3}
12: {1,1,2}
14: {1,4}
18: {1,2,2}
22: {1,5}
26: {1,6}
30: {1,2,3}
34: {1,7}
36: {1,1,2,2}
38: {1,8}
40: {1,1,1,3}
42: {1,2,4}
46: {1,9}
58: {1,10}
60: {1,1,2,3}
62: {1,11}
MATHEMATICA
Select[Range[100], #==1||SubsetQ[PrimePi/@First/@FactorInteger[#], Last/@FactorInteger[#]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 18 2019
STATUS
approved