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A338330
Numbers that are neither a power of a prime (A000961) nor is their set of distinct prime indices pairwise coprime.
3
21, 39, 42, 57, 63, 65, 78, 84, 87, 91, 105, 111, 114, 115, 117, 126, 129, 130, 133, 147, 156, 159, 168, 171, 174, 182, 183, 185, 189, 195, 203, 210, 213, 222, 228, 230, 231, 234, 235, 237, 247, 252, 258, 259, 260, 261, 266, 267, 273, 285, 294, 299, 301
OFFSET
1,1
COMMENTS
Also Heinz numbers of partitions that are neither constant (A144300) nor have pairwise coprime distinct parts (A304709), hence the formula. The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), giving a bijective correspondence between positive integers and integer partitions.
FORMULA
Equals A024619 \ A304711.
EXAMPLE
The sequence of terms together with their prime indices begins:
21: {2,4} 126: {1,2,2,4} 203: {4,10}
39: {2,6} 129: {2,14} 210: {1,2,3,4}
42: {1,2,4} 130: {1,3,6} 213: {2,20}
57: {2,8} 133: {4,8} 222: {1,2,12}
63: {2,2,4} 147: {2,4,4} 228: {1,1,2,8}
65: {3,6} 156: {1,1,2,6} 230: {1,3,9}
78: {1,2,6} 159: {2,16} 231: {2,4,5}
84: {1,1,2,4} 168: {1,1,1,2,4} 234: {1,2,2,6}
87: {2,10} 171: {2,2,8} 235: {3,15}
91: {4,6} 174: {1,2,10} 237: {2,22}
105: {2,3,4} 182: {1,4,6} 247: {6,8}
111: {2,12} 183: {2,18} 252: {1,1,2,2,4}
114: {1,2,8} 185: {3,12} 258: {1,2,14}
115: {3,9} 189: {2,2,2,4} 259: {4,12}
117: {2,2,6} 195: {2,3,6} 260: {1,1,3,6}
MATHEMATICA
Select[Range[2, 100], !PrimePowerQ[#]&&!CoprimeQ@@Union[PrimePi/@First/@FactorInteger[#]]&]
CROSSREFS
A338331 is the complement.
A304713 is the complement of the version for divisibility.
Sequence in context: A307278 A176071 A072708 * A102478 A221048 A182297
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 12 2020
STATUS
approved