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A328868
Heinz numbers of integer partitions with no two (not necessarily distinct) parts relatively prime, but with no divisor in common to all of the parts.
5
17719, 40807, 43381, 50431, 74269, 83143, 101543, 105703, 116143, 121307, 123469, 139919, 140699, 142883, 171613, 181831, 185803, 191479, 203557, 205813, 211381, 213239, 215267, 219271, 230347, 246703, 249587, 249899, 279371, 286897, 289007, 296993, 300847
OFFSET
1,1
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
EXAMPLE
The sequence of terms together with their prime indices begins:
17719: {6,10,15}
40807: {6,14,21}
43381: {6,15,20}
50431: {10,12,15}
74269: {6,10,45}
83143: {10,15,18}
101543: {6,21,28}
105703: {6,15,40}
116143: {12,14,21}
121307: {10,15,24}
123469: {12,15,20}
139919: {6,15,50}
140699: {6,22,33}
142883: {6,10,75}
171613: {6,14,63}
181831: {6,20,45}
185803: {10,14,35}
191479: {14,18,21}
203557: {15,18,20}
205813: {10,15,36}
211381: {10,12,45}
213239: {6,15,70}
215267: {6,10,105}
219271: {6,26,39}
230347: {6,6,10,15}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
dv=Select[Range[100000], GCD@@primeMS[#]==1&&And[And@@(GCD[##]>1&)@@@Tuples[Union[primeMS[#]], 2]]&]
CROSSREFS
These are the Heinz numbers of the partitions counted by A202425.
Terms of A328679 that are not powers of 2.
The strict case is A318716 (preceded by 2).
A ranking using binary indices (instead of prime indices) is A326912.
Heinz numbers of relatively prime partitions are A289509.
Sequence in context: A187641 A252624 A252513 * A322552 A235023 A133540
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 30 2019
STATUS
approved