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A356845
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Odd numbers with gapless prime indices.
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7
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1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25, 27, 29, 31, 35, 37, 41, 43, 45, 47, 49, 53, 59, 61, 67, 71, 73, 75, 77, 79, 81, 83, 89, 97, 101, 103, 105, 107, 109, 113, 121, 125, 127, 131, 135, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 175, 179, 181, 191
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OFFSET
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1,2
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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.
A sequence is gapless if it covers an interval of positive integers.
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LINKS
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EXAMPLE
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The terms together with their prime indices begin:
1: {}
3: {2}
5: {3}
7: {4}
9: {2,2}
11: {5}
13: {6}
15: {2,3}
17: {7}
19: {8}
23: {9}
25: {3,3}
27: {2,2,2}
29: {10}
31: {11}
35: {3,4}
37: {12}
41: {13}
43: {14}
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
nogapQ[m_]:=Or[m=={}, Union[m]==Range[Min[m], Max[m]]];
Select[Range[1, 100, 2], nogapQ[primeMS[#]]&]
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CROSSREFS
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Consists of the odd terms of A073491.
These partitions are counted by A264396.
A356233 counts factorizations into gapless numbers.
Cf. A003963, A034296, A055932, A073493, A107428, A287170, A289508, A325160, A356231, A356234, A356841.
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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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