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A355537
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Number of ways to choose a sequence of prime factors, one of each integer from 2 to n.
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4
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1, 1, 1, 1, 1, 2, 2, 2, 2, 4, 4, 8, 8, 16, 32, 32, 32, 64, 64, 128, 256, 512, 512, 1024, 1024, 2048, 2048, 4096, 4096, 12288, 12288, 12288, 24576, 49152, 98304, 196608, 196608, 393216, 786432, 1572864, 1572864, 4718592, 4718592, 9437184, 18874368, 37748736
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OFFSET
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1,6
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COMMENTS
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Also partial products of A001221 without the first term 0, sum A013939.
For initial terms up to n = 29 we have a(n) = 2^A355538(n). The first non-power of 2 is a(30) = 12288.
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LINKS
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EXAMPLE
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The a(n) choices for n = 2, 6, 10, 12, with prime(k) replaced by k:
(1) (12131) (121314121) (12131412151)
(12132) (121314123) (12131412152)
(121324121) (12131412351)
(121324123) (12131412352)
(12132412151)
(12132412152)
(12132412351)
(12132412352)
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MATHEMATICA
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Table[Times@@PrimeNu/@Range[2, m], {m, 2, 30}]
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CROSSREFS
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The sum of the same integers is A000096.
The version for divisors instead of prime factors is A066843.
The integers themselves are the rows of A131818.
The version with multiplicity is A327486.
Using prime indices instead of 2..n gives A355741, for multisets A355744.
Counting sequences instead of multisets gives A355746.
A001222 counts prime factors with multiplicity.
A003963 multiplies together the prime indices of n.
Cf. A000005, A000040, A000720, A002110, A013939, A076610, A355538, A355731, A355733, A355745, A355747.
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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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