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A355735
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Number of ways to choose a divisor of each prime index of n (taken in weakly increasing order) such that the result is weakly increasing.
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15
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1, 1, 2, 1, 2, 2, 3, 1, 3, 2, 2, 2, 4, 3, 3, 1, 2, 3, 4, 2, 5, 2, 3, 2, 3, 4, 4, 3, 4, 3, 2, 1, 3, 2, 4, 3, 6, 4, 7, 2, 2, 5, 4, 2, 4, 3, 4, 2, 6, 3, 3, 4, 5, 4, 3, 3, 7, 4, 2, 3, 6, 2, 7, 1, 6, 3, 2, 2, 5, 4, 6, 3, 4, 6, 4, 4, 4, 7, 4, 2, 5, 2, 2, 5, 3, 4, 7
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OFFSET
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1,3
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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(15) = 3 ways are: (1,1), (1,3), (2,3).
The a(18) = 3 ways are: (1,1,1), (1,1,2), (1,2,2).
The a(2) = 1 through a(19) = 4 ways:
1 1 11 1 11 1 111 11 11 1 111 1 11 11 1111 1 111 1
2 3 12 2 12 13 5 112 2 12 13 7 112 2
4 22 3 14 23 122 4
6 8
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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]], LessEqual@@#&]], {n, 100}]
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CROSSREFS
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Choosing a multiset instead of sequence gives A355733, firsts A355734.
Positions of first appearances are A355736.
A003963 multiplies together the prime indices of n.
A061395 selects the maximum prime index.
A120383 lists numbers divisible by all of their prime indices.
A324850 lists numbers divisible by the product of their prime indices.
Cf. A000720, A076610, A316524, A335433, A335448, A340827, A340852, A344616, A355737, A355739, A355740, A355742.
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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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