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A355535
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Odd numbers of which it is not possible to choose a different prime factor of each prime index.
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13
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9, 21, 25, 27, 45, 49, 57, 63, 75, 81, 99, 105, 115, 117, 121, 125, 133, 135, 147, 153, 159, 171, 175, 189, 195, 207, 225, 231, 243, 245, 261, 273, 275, 279, 285, 289, 297, 315, 325, 333, 343, 345, 351, 357, 361, 363, 369, 371, 375, 387, 393, 399, 405, 423
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OFFSET
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1,1
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
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LINKS
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EXAMPLE
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The terms together with their prime indices begin:
9: {2,2}
21: {2,4}
25: {3,3}
27: {2,2,2}
45: {2,2,3}
49: {4,4}
57: {2,8}
63: {2,2,4}
75: {2,3,3}
81: {2,2,2,2}
99: {2,2,5}
105: {2,3,4}
For example, the prime indices of 897 are {2,6,9}, of which we can choose prime factors in two ways: (2,2,3) or (2,3,3); but neither of these has all distinct elements, so 897 is in the sequence.
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], OddQ[#]&&Select[Tuples[primeMS/@primeMS[#]], UnsameQ@@#&]=={}&]
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CROSSREFS
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The version for all divisors including evens is A355740, zeros of A355739.
Choices of a prime factor of each prime index: A355741, unordered A355744.
A001222 counts prime factors with multiplicity.
A003963 multiplies together the prime indices of n.
A120383 lists numbers divisible by all of their prime indices.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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