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A356069
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Number of divisors of n whose prime indices cover an interval of positive integers (A073491).
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14
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1, 2, 2, 3, 2, 4, 2, 4, 3, 3, 2, 6, 2, 3, 4, 5, 2, 6, 2, 4, 3, 3, 2, 8, 3, 3, 4, 4, 2, 7, 2, 6, 3, 3, 4, 9, 2, 3, 3, 5, 2, 5, 2, 4, 6, 3, 2, 10, 3, 4, 3, 4, 2, 8, 3, 5, 3, 3, 2, 10, 2, 3, 4, 7, 3, 5, 2, 4, 3, 5, 2, 12, 2, 3, 6, 4, 4, 5, 2, 6, 5, 3, 2, 7, 3, 3
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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.
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LINKS
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EXAMPLE
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The a(n) counted divisors of n = 1, 2, 4, 6, 12, 16, 24, 30, 36, 48, 72, 90:
1 2 4 6 12 16 24 30 36 48 72 90
1 2 3 6 8 12 15 18 24 36 45
1 2 4 4 8 6 12 16 24 30
1 3 2 6 5 9 12 18 18
2 1 4 3 6 8 12 15
1 3 2 4 6 9 9
2 1 3 4 8 6
1 2 3 6 5
1 2 4 3
1 3 2
2 1
1
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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_]:=m=={}||Union[m]==Range[Min[m], Max[m]];
Table[Length[Select[Divisors[n], nogapQ[primeMS[#]]&]], {n, 100}]
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CROSSREFS
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The complement in the initial case is counted by A356225.
A328338 has third-largest divisor prime.
A356226 gives the lengths of maximal gapless intervals of 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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