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A355737
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Number of ways to choose a sequence of divisors, one of each prime index of n (with multiplicity), such that the result has no common divisor > 1.
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28
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0, 1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 2, 1, 3, 4, 1, 1, 4, 1, 2, 4, 2, 1, 2, 3, 4, 7, 3, 1, 4, 1, 1, 4, 2, 6, 4, 1, 4, 6, 2, 1, 6, 1, 2, 8, 3, 1, 2, 5, 4, 4, 4, 1, 8, 4, 3, 5, 4, 1, 4, 1, 2, 10, 1, 6, 4, 1, 2, 6, 6, 1, 4, 1, 6, 8, 4, 6, 8, 1, 2, 15, 2, 1, 6, 4, 4
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OFFSET
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1,6
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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(2) = 1 through a(18) = 4 choices:
1 1 11 1 11 1 111 11 11 1 111 1 11 11 1111 1 111
12 12 13 112 12 13 112
21 14 21 121
23 122
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Length[Select[Tuples[Divisors/@primeMS[n]], GCD@@#==1&]], {n, 100}]
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CROSSREFS
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For weakly increasing instead of coprime we have A355735, primes A355745.
Positions of first appearances are A355738.
A001222 counts prime factors with multiplicity.
A003963 multiplies together the prime indices of n.
A120383 lists numbers divisible by all of their prime indices.
A289508 gives GCD of prime indices.
A324850 lists numbers divisible by the product of their prime indices.
Cf. A000720, A007359, A051424, A076610, A289507, A296150, A302696, A302698, A355733, A355744, A355748.
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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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