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A355747
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Number of multisets that can be obtained by choosing a divisor of each positive integer from 1 to n.
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9
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1, 1, 2, 4, 10, 20, 58, 116, 320, 772, 2170, 4340, 14112, 28224, 78120, 212004, 612232, 1224464, 3873760, 7747520, 24224608, 64595088, 175452168, 350904336
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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The a(0) = 1 through a(4) = 10 multisets:
{} {1} {1,1} {1,1,1} {1,1,1,1}
{1,2} {1,1,2} {1,1,1,2}
{1,1,3} {1,1,1,3}
{1,2,3} {1,1,1,4}
{1,1,2,2}
{1,1,2,3}
{1,1,2,4}
{1,1,3,4}
{1,2,2,3}
{1,2,3,4}
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MATHEMATICA
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Table[Length[Union[Sort/@Tuples[Divisors/@Range[n]]]], {n, 0, 10}]
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PROG
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(Python)
from sympy import divisors
from itertools import count, islice
def agen():
s = {tuple()}
for n in count(1):
yield len(s)
s = set(tuple(sorted(t+(d, ))) for t in s for d in divisors(n))
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CROSSREFS
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The sum of the same integers is A000096.
Counting sequences instead of multisets gives A066843.
The integers themselves are the rows of A131818 (shifted).
For prime factors instead of divisors we have A355746, factors A355537.
A001222 counts prime factors with multiplicity.
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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